Velocity-time graph — Science definition

A graph of velocity versus time; its slope is the acceleration and the area beneath it is the displacement.

Where it is taught

In use

On a velocity-time graph, slope gives acceleration and signed area gives displacement.

Motion Graphs & Kinematic Equations

Questions using velocity-time graph

Problem 1

A velocity-time graph shows an object moving at a constant 6 m/s from t = 0 to t = 5.0 s. What displacement occurred during that time?
Answer and explanation

30 m

Displacement is the area under the velocity-time graph: 6 × 5.0 = 30 m.

Problem 2

Describe how you would find (a) an object's velocity from a position-time graph and (b) its displacement from a velocity-time graph.
Answer and explanation

(a) Velocity is the slope of the position-time graph — pick two points on the line and compute rise over run (change in position divided by change in time). (b) Displacement is the area between the velocity-time line and the time axis; for simple shapes you find the area of the rectangle, triangle, or trapezoid the graph forms.

Problem 3

A velocity-time graph shows an object at a constant 8 m/s for 6.0 s. What displacement occurred?
Answer and explanation

48 m

Displacement is the area under the graph: 8 × 6.0 = 48 m.

Problem 4

On a velocity-time graph, the area between the line and the time axis represents the object's…
  1. jerk
  2. acceleration
  3. velocity
  4. displacement
Answer and explanation

displacement

Velocity multiplied by time gives displacement, so the area under a velocity-time graph is the displacement.

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