Speed, Velocity & Acceleration — Print · Grade 8 Science

Speed, Velocity & Acceleration

Learning goals

I can calculate average speed using speed = distance ÷ time.
I can distinguish speed, velocity, and acceleration, and calculate acceleration from a change in velocity over time.

Readings for this unit

A soft bumper stops a toy differently

Before this unit

Divide distance by time and include direction when needed.

Use three teaching sessions of about 40–45 minutes: first observe the phenomenon, draft a model and study Parts 1–2; next explain Parts 3–4 with the figures and evidence; then work the application, examples, practice, model revision and exit check. Divide any difficult part into smaller steps and revisit after feedback. Investigations, review and quizzes have separate sessions. Study the four visual parts across the scheduled sessions, then use the illustrated worked case and independent transfer questions. Extend or revisit a session when the learner cannot explain the figure; completion time is a proposed allocation, not a mastery guarantee.

Start with something to explain

What would explain the observations in speed, velocity & acceleration?

Illustrative evidence case. An illustrative walk covers 30 m east and then 10 m west in 20 s. The starting position is the chosen origin, with east positive.

The path covers 30 m east and 10 m west, for 40 m distance and 20 m east displacement. Arrows separate the journey from the start-to-finish comparison. The schematic horizontal positions are not a precision scale and do not establish a changing speed without elapsed-time data.

Notice and wonder

Over 20 s, what are average speed and velocity? Write two observations from the supplied record without guessing their cause. Include a quantity and its unit when given. An observation is what was recorded; an inference is what you think explains it.

Write one question about why the pattern occurs and one question about a comparison that could distinguish competing explanations. A testable question identifies what could be observed or measured.

Your first model

Before reading the model answer, sketch the named objects or particles and label what you think changes. Find distance, displacement, average speed and average velocity. Explain why the two rates differ. Keep this first version so you can compare it with your later explanation.

Build the language from the idea

speed: How fast an object moves, found by dividing distance traveled by the time it took.
velocity: Speed in a specific direction, like 60 km/h north.
acceleration: How quickly velocity changes over time, found by dividing the change in velocity by the time it took.
model: A representation that explains selected features and makes predictions; it leaves other details out.
evidence: Relevant observations or records used to support or challenge a claim.
system boundary: The chosen limit separating the objects being studied from their surroundings.
assumption: A condition taken as true for a model or calculation and needing to be checked against the case.

Speed answers the everyday question, 'how fast is something moving?' You calculate it by dividing the distance traveled by the time it took: speed = distance ÷ time. If a cyclist rides 24 km in 3 hours, her average speed is 24 ÷ 3 = 8 km/h. That word 'average' matters, because she probably sped up on the flats and slowed on the hills — average speed smooths all of that into a single number for the whole trip.

Velocity takes speed and adds one crucial extra piece of information: direction. '8 km/h' is a speed, but '8 km/h heading north' is a velocity. This might sound like a fussy distinction, but it's a big deal in the real world. Two cars can share the exact same speed yet have completely different velocities if they're pointed different ways — and that difference is everything when they're both approaching the same intersection. Anytime an object turns, its velocity is changing even if its speed stays constant.

Acceleration measures how quickly velocity is changing — how fast you're speeding up, slowing down, or turning. Its formula is acceleration = (final velocity − initial velocity) ÷ time. Because it describes a change in velocity spread over a stretch of time, acceleration carries units like m/s² (meters per second, per second). A car that goes from 10 m/s to 25 m/s in 5 seconds is accelerating at (25 − 10) ÷ 5 = 3 m/s².

Acceleration can be positive or negative once a direction has been chosen positive. Its sign gives direction, not whether speed increases. With right positive, a right-moving cart with negative acceleration initially slows, while a left-moving cart with negative acceleration speeds up. Compare velocity and acceleration directions. Changing direction around a curve also changes velocity even if speed stays constant.

The arrows distinguish present motion from change in motion. When velocity and acceleration point in the same direction, speed increases. Opposite directions initially reduce speed. In the third row both signed quantities are negative, yet the object speeds up to the left. The sign depends on the chosen coordinate direction. This compares straight-line cases; turning also changes velocity even when speed stays constant.

Keeping these three ideas straight is the backbone of describing any kind of motion. Speed tells you the pace, velocity pins down the pace and the heading, and acceleration captures how that motion is changing from moment to moment. Engineers use exactly these quantities to time traffic lights, design safe highway on-ramps, and figure out how much room a car needs to stop — the same math a radar gun uses to clock a driver going over the limit.

Acceleration is change in velocity divided by elapsed time. Direction matters: a cart moving right and slowing has acceleration left. The sign of acceleration alone does not tell you whether speed increases; compare it with the velocity direction.

Keep units consistent before calculating. If position is in meters and time in seconds, speed is in m/s and acceleration in m/s². State an average when data cover an interval, since an average can hide different motions within it.

Build your understanding

Where this fits

This unit helps answer the chapter question: What evidence lets us describe and predict motion? Keep a notebook table with the question, evidence, explanation and one unresolved issue. Revise a previous model only when you can name the new evidence or idea that changes it.

Part 1 · Choose a reference and describe the path

Motion is a change in position relative to a chosen reference. Distance measures total path length; displacement compares final and initial position and includes direction. A return trip can have substantial distance with zero displacement. State the reference and positive direction before using signed positions.

Read the visual model

How can a trip have zero displacement without zero distance?

Visual reasoning — after your attempt

The final position can equal the initial position even after a nonzero path. Displacement uses endpoints; distance adds the traveled path.

A student walks 6 m east and 6 m west back to the start. Distance is 12 m; displacement is zero. Mark the route and endpoints separately so the calculation answers the intended question.

Pause and explain

How can a trip have zero displacement without zero distance?

Check your reasoning after answering

The final position can equal the initial position even after a nonzero path. Displacement uses endpoints; distance adds the traveled path.

Part 2 · Distinguish average speed from average velocity

Average speed is total distance divided by elapsed time. Average velocity is displacement divided by elapsed time and includes direction. Both describe an interval, not every instant within it. A stopwatch result alone cannot show whether the object moved steadily, stopped, or changed pace.

Two measurements of one journey that answer different questions. A runner finishing a lap has covered a distance and has zero displacement, which is why average velocity for the lap is zero and average speed is not.

Read the visual model

Does a 2 m/s average speed establish a constant 2 m/s at every moment?

Visual reasoning — after your attempt

No. Different speeds and stops can produce the same distance/time average. More detailed position or speed measurements are needed.

For the 12 m return trip lasting 6 s, average speed is 2 m/s and average velocity is zero. A zero average velocity does not imply the student stood still throughout the six seconds.

Pause and explain

Does a 2 m/s average speed establish a constant 2 m/s at every moment?

Check your reasoning after answering

No. Different speeds and stops can produce the same distance/time average. More detailed position or speed measurements are needed.

Part 3 · Recognize three ways velocity can change

Acceleration is change in velocity divided by time over a specified interval. It can describe speeding up, slowing down, or changing direction. Choose a sign convention; negative acceleration means the acceleration points in the negative direction, not automatically that speed is decreasing.

Read the visual model

Can motion at constant speed still involve acceleration?

Visual reasoning — after your attempt

Yes. Changing direction changes velocity, so curved motion can be accelerated even when the speed remains constant.

A car traveling around a bend at constant speed still changes velocity because direction changes. A right-moving cart with leftward acceleration initially slows; a left-moving cart with leftward acceleration speeds up. Label both arrows.

The blue and red arrows carry different units: velocity in m/s and acceleration in m/s². Compare directions rather than adding their lengths. A negative velocity means motion left in this reference; a negative acceleration means a change toward the left. If both are negative, the object can move left faster. A cart moving right with leftward acceleration may slow to rest and later move left; the description depends on the interval.

Pause and explain

Can motion at constant speed still involve acceleration?

Check your reasoning after answering

Yes. Changing direction changes velocity, so curved motion can be accelerated even when the speed remains constant.

Part 4 · Calculate an interval and check its meaning

Use average acceleration=(final velocity−initial velocity)/time. Include direction or signs and units m/s². The unit describes change in m/s per second, not a traveled distance. An average calculation does not establish constant acceleration during the entire interval.

For this modeled constant-acceleration cart, velocity rises from 2 to 8 m/s in 3 s. The graph slope is (8−2)/(3−0) = 2 m/s². The units mean velocity changes by 2 m/s each second. A velocity–time graph uses slope for acceleration, whereas a position–time graph uses slope for velocity. If only the endpoints were measured, this slope would establish an average rather than prove the straight line at every instant.

Read the visual model

Why is m/s² appropriate for acceleration?

Visual reasoning — after your attempt

Velocity changes in m/s and is divided by seconds. The resulting unit describes how much velocity changes per second.

A cart changes from 2 m/s right to 8 m/s right in 3 s. With right positive, average acceleration is (8−2)/3=2 m/s² right. Confirm that the velocity increased by 6 m/s over the stated three seconds.

To read the slope, choose two points on the velocity–time graph, subtract their velocities, then divide by their time difference. Here the rise is 6 m/s and the run is 3 s. The result 2 m/s² describes a rate of velocity change. The graph is a straight line only because constant acceleration was assumed in this illustration; endpoint records alone establish an average.

Pause and explain

Why is m/s² appropriate for acceleration?

Check your reasoning after answering

Velocity changes in m/s and is divided by seconds. The resulting unit describes how much velocity changes per second.

Apply the whole unit · Analyze a journey and a speeding cart

Illustrative journey: 8 m east then 2 m west in 5 s. Separate cart record: velocity changes from 1 m/s east to 7 m/s east in 3 s. Take east as positive.

Your task

Find journey distance, displacement, average speed, and average velocity; then find the cart’s average acceleration. Draw direction arrows and explain why the interval averages do not establish constant motion.

What your response should show

Use the supplied observations and measurements accurately; include units where needed.
Explain the science behind your answer, rather than giving only a number or label.
Show a labeled model, calculation, or evidence comparison as requested.
State an assumption or limitation and suggest a useful next measurement.

Response guidance — after your attempt

Distance=10 m; displacement=6 m east; average speed=2 m/s; average velocity=1.2 m/s east. Cart acceleration=(7−1)/3=2 m/s² east. More detailed readings are needed to determine within-interval changes. Keep journey and cart evidence separate; they are different records.

Scientific references and adapted teaching resources

Parent / teacher teaching notes

Begin with a drawn route before equations. Ask distance or displacement on every division-by-time task. Use a turning example to distinguish speed from velocity. Adaptation credit: OpenSciEd middle-school teaching routines and public task structures by OpenSciEd, CC BY 4.0. This independent version adds original explanatory text, data and figures, terminology support and a home-study schedule. It does not reproduce the complete teacher editions or their classroom validation.

The key idea

Speed = distance ÷ time; velocity adds direction; acceleration = change in velocity ÷ time.

Speed

speed = distance ÷ time

distance in meters or km; time in seconds, minutes, or hours; speed in matching units like m/s or km/h.

Acceleration

a = (v final − v initial) ÷ t

v final and v initial are velocities in m/s; t is time in seconds; a comes out in m/s².

Worked examples

Example 1

A cyclist travels 24 km in 3 hours. What is her average speed?

Use speed = distance ÷ time.
24 ÷ 3 = 8.

Answer: 8 km/h

Example 2 · Worked application

A runner travels 120 m east, then 120 m west in 60 s. Compare average speed and average velocity.

Total distance=240 m, so average speed=240/60=4 m/s.
Final position equals initial position, so displacement=0 m.
Average velocity=displacement/time=0 m/s.

Answer: Average speed 4 m/s; average velocity 0 m/s.

Check the reasoning

Distance counts the whole path; displacement compares endpoints.

Example 3

A car speeds up from 10 m/s to 25 m/s in 5 seconds. What is its acceleration?

Use acceleration = (final velocity − initial velocity) ÷ time.
(25 − 10) ÷ 5 = 15 ÷ 5.
= 3.

Answer: 3 m/s²

Example 4

A student walks 30 m east then 30 m west in 40 s. Find average speed and average velocity.

Total distance=60 m; speed=60/40=1.5 m/s.
Displacement=0 m; average velocity=0/40=0 m/s.

Answer: Average speed 1.5 m/s; average velocity 0 m/s.

Example 5 · Find and fix the mistake

Context: A runner travels 120 m east, then 120 m west in 60 s. Compare average speed and average velocity. A student claims: “Negative acceleration always means slowing down.” Evaluate the claim and write a corrected explanation.

Test the claim against the stated conditions: Distance counts the whole path; displacement compares endpoints.
The sign depends on the chosen axis. An object moving in the negative direction speeds up if acceleration is also negative.

Answer: The sign depends on the chosen axis. An object moving in the negative direction speeds up if acceleration is also negative.

Check the reasoning

Distance counts the whole path; displacement compares endpoints.

Example 6 · Interpret the visual model

How can a trip have zero displacement without zero distance?

Identify the represented objects, axes, labeled quantities and stated conditions before choosing a rule.
A student walks 6 m east and 6 m west back to the start. Distance is 12 m; displacement is zero. Mark the route and endpoints separately so the calculation answers the intended question.
The final position can equal the initial position even after a nonzero path. Displacement uses endpoints; distance adds the traveled path.

Answer: The final position can equal the initial position even after a nonzero path. Displacement uses endpoints; distance adds the traveled path.

Check the reasoning

Keep the model’s stated limits explicit: The path covers 30 m east and 10 m west, for 40 m distance and 20 m east displacement. Arrows separate the journey from the start-to-finish comparison. The schematic horizontal positions are not a precision scale and do not establish a changing speed without elapsed-time data.

Avoid these mistakes

A negative acceleration does not always mean an object is slowing down.

Check your understanding

A student walks 30 m east then 30 m west in 40 s. Find average speed and average velocity.

Discuss the answer

Average speed 1.5 m/s; average velocity 0 m/s.

Can an object accelerate while its speed remains constant?

Discuss the answer

Average speed uses total distance divided by elapsed time. Average velocity uses displacement divided by elapsed time and includes direction. A round trip can have a nonzero average speed but zero average velocity because the final position equals the starting position. Acceleration is change in velocity divided by elapsed time. Direction matters: a cart moving right and slowing has acceleration left. The sign of acceleration alone does not tell you whether speed increases; compare it with the velocity direction.

Return to the phenomenon

An illustrative walk covers 30 m east and then 10 m west in 20 s. The starting position is the chosen origin, with east positive. Find distance, displacement, average speed and average velocity. Explain why the two rates differ. Revise your first explanation using a named idea from the lesson. Mark the changed part and the evidence that supports it.

Compare explanations after your attempt

Distance is 40 m; displacement is +20 m east. Average speed is 40/20=2 m/s; average velocity is +20/20=+1 m/s east. Distance counts the full path, while displacement compares final and initial positions with direction. These averages do not establish a constant speed at every instant.

What should we investigate next?

Which condition could be changed to test a remaining uncertainty in this explanation? State the predicted observation and what result would challenge your model.

Investigate, explain and revise

Use these tasks after the three teaching sessions as needed. Discuss an attempted explanation before opening response guidance; a matching sentence is less important than a supported mechanism.

Activity 1 · Explain the new evidence case

Assigned reading and preparation

Use the visible scenario above, Parts 1–4 and your first notebook model. No outside reading or equipment is required.

Your task

An illustrative walk covers 30 m east and then 10 m west in 20 s. The starting position is the chosen origin, with east positive. Find distance, displacement, average speed and average velocity. Explain why the two rates differ. Write 100–150 words or give a labeled drawing with an equivalent oral explanation.

Success criteria

Use two relevant stated records or conditions.
Explain the mechanism rather than only repeat a definition.
Label observation and inference.
Name a changed model feature or a remaining uncertainty.

Hint

Read the stated boundary and conditions before selecting a relationship. The unit’s worked examples show intermediate steps.

Response guidance — discuss after your attempt

Activity 2 · Read and extend the figure

Assigned reading and preparation

Study the new labeled figure and its caption, then compare it with the associated teaching part.

Your task

Over 20 s, what are average speed and velocity? Explain what each important label represents. Add one missing feature that would be needed for a different question, and explain why the original figure leaves it out.

Success criteria

Answer the figure question with its stated labels.
Connect the visual representation to the scientific idea.
Identify a specific limitation from the caption.
Propose a useful change without misrepresenting supplied evidence.

Hint

Response guidance — discuss after your attempt

Average speed is 40/20=2 m/s; average velocity is 20/20=1 m/s east. The path covers 30 m east and 10 m west, for 40 m distance and 20 m east displacement. Arrows separate the journey from the start-to-finish comparison. The schematic horizontal positions are not a precision scale and do not establish a changing speed without elapsed-time data.

Words to know

speed: How fast an object moves, found by dividing distance traveled by the time it took.
velocity: Speed in a specific direction, like 60 km/h north.
acceleration: How quickly velocity changes over time, found by dividing the change in velocity by the time it took.
model: A representation that explains selected features and makes predictions; it leaves other details out.
evidence: Relevant observations or records used to support or challenge a claim.
system boundary: The chosen limit separating the objects being studied from their surroundings.
assumption: A condition taken as true for a model or calculation and needing to be checked against the case.

Average speed vs. the number on your speedometer

The speed = distance ÷ time formula gives you average speed over a whole trip, smoothing out every stoplight and highway stretch into one number. But your car's speedometer shows instantaneous speed — how fast you're going at that exact moment, which can be very different from the average. A trip with an average speed of 40 km/h might have included stretches at 0 km/h (stopped at lights) and 70 km/h (open highway); average speed just cannot capture that up-and-down detail, which is exactly why scientists use graphs to show motion changing moment to moment.

Reading motion straight off a graph

If you plot an object's distance against time, the slope (steepness) of that line is literally its speed — a steeper line means faster motion, and a flat line means the object has stopped. Plot velocity against time instead, and the slope becomes acceleration: a rising line means speeding up, a falling line means slowing down, and a flat line means constant velocity (zero acceleration). This is one of the most useful shortcuts in physics: instead of doing arithmetic, you can often just look at how steep — and which way — a graph tilts.

Galileo's ramps: clocking acceleration before stopwatches existed

In the early 1600s, Galileo Galilei wanted to study how falling objects accelerate, but free fall happens too fast to time accurately with the water clocks and pulse-counting available then. His clever workaround: roll a ball down a gently sloped ramp, which 'dilutes' gravity's pull and slows everything down enough to measure. By timing balls rolling different distances, Galileo showed that acceleration due to gravity is constant and doesn't depend on an object's weight — centuries before anyone had a precise clock, let alone a computer.

Acceleration is sneakier than 'speeding up' — turning counts too

Because velocity includes direction, any change in direction is technically acceleration — even if speed never changes at all. A car rounding a curve at a perfectly steady 50 km/h is still accelerating, because its direction is constantly changing; this is called centripetal acceleration. Pilots and astronauts describe strong accelerations in multiples of Earth's gravity, or 'g-forces' — a fighter jet pulling a tight turn might subject its pilot to 6–9 g's, meaning their body effectively feels 6 to 9 times heavier than normal, even though their speed might barely change.

In the real world

Traffic radar guns calculate a car's speed to catch drivers going faster than the posted limit.

Exit check

Over 20 s, what are average speed and velocity? Explain the relevant mechanism and one model limitation.

Check your explanation after answering

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Problem 1

A runner covers 100 meters in 20 seconds. What is the average speed?

Answer and explanation

5 m/s

Speed = distance ÷ time = 100 ÷ 20 = 5 m/s.

Problem 2

A train travels 300 km in 4 hours. What is its average speed?

Answer and explanation

75 km/h

Speed = distance ÷ time = 300 ÷ 4 = 75 km/h.

Problem 3

A skateboarder speeds up from 2 m/s to 8 m/s in 3 seconds. Find the acceleration.

Answer and explanation

2 m/s²

Acceleration = (8 − 2) ÷ 3 = 6 ÷ 3 = 2 m/s².

Problem 4

Which quantity includes BOTH speed and direction?

distance
velocity
time
mass

Answer and explanation

velocity

Velocity is speed given with a direction.

Problem 5

Explain the difference between speed and velocity using an example.

Answer and explanation

Speed only tells you how fast something is moving, like 50 km/h. Velocity tells you how fast AND in what direction, like 50 km/h north. Two cars traveling the same speed in opposite directions have the same speed but different velocities.

Problem 6

A car slows from 30 m/s to 10 m/s in 4 seconds. What is its acceleration? (Include the correct sign.)

Answer and explanation

-5 m/s²

Acceleration = (10 − 30) ÷ 4 = −20 ÷ 4 = −5 m/s². The negative sign shows it's slowing down.

Problem 7

A student walks 30 m east then 30 m west in 40 s. Find average speed and average velocity. Explain the reasoning in your own words.

Answer and explanation

Average speed 1.5 m/s; average velocity 0 m/s.

Total distance=60 m; speed=60/40=1.5 m/s.

Displacement=0 m; average velocity=0/40=0 m/s.

Response criteria

Use the stated conditions.
Show the evidence or calculation.
Explain the conclusion and any stated limitation.

Problem 8

A cyclist covers 180 m in 30 s. Calculate average speed. Show the reasoning, not just the conclusion.

Hints

Distance counts the whole path; displacement compares endpoints.

Answer and explanation

180/30=6 m/s.

Problem 9

Velocity changes from 2 m/s east to 10 m/s east in 4 s. Calculate average acceleration.

Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

(10−2)/4=2 m/s² east, assuming east is positive.

Problem 10

Right is positive. A cart changes velocity from −2 to −8 m/s in 3 s. Calculate average acceleration and explain whether it speeds up or slows down.

Answer and explanation

(−8−(−2))/3 = −2 m/s². It speeds up toward the left because speed rises from 2 to 8 m/s.

Subtract signed velocities before dividing.

Compare velocity direction with acceleration direction.

Response criteria

Calculate −2 m/s².
Explain leftward motion.
Reject negative-always-slows.

Problem 11

For this unit’s illustrated case, how can a trip have zero displacement without zero distance?

Answer and explanation

The final position can equal the initial position even after a nonzero path. Displacement uses endpoints; distance adds the traveled path.

A student walks 6 m east and 6 m west back to the start. Distance is 12 m; displacement is zero. Mark the route and endpoints separately so the calculation answers the intended question.

The final position can equal the initial position even after a nonzero path. Displacement uses endpoints; distance adds the traveled path.

Response criteria

Use the named labels, directions or supplied quantities accurately.
Connect the visual evidence to the scientific mechanism or calculation.
State the relevant model conditions or limitation.

Problem 12

Right is positive. A cart’s velocity changes from −3 to −9 m/s in 2 s. Find average acceleration and explain its speed change.

Answer and explanation

Average acceleration = (−9−(−3))/2 = −3 m/s²; speed increases leftward from 3 to 9 m/s. Negative acceleration does not always mean slowing.

Subtract signed velocities.

Compare the magnitudes and directions instead of using a sign slogan.

Average acceleration = (−9−(−3))/2 = −3 m/s²; speed increases leftward from 3 to 9 m/s. Negative acceleration does not always mean slowing.

Response criteria

Use the named labels, directions or supplied quantities accurately.
Connect the visual evidence to the scientific mechanism or calculation.
State the relevant model conditions or limitation.

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