Lesson Worksheet: Velocity–Time Graphs Mathematics

In this worksheet, we will practice calculating the displacement or acceleration of a particle moving in a straight line from its velocity–time graph.

Q1:

The given velocity-time graph represents a particle moving in a straight line. Determine its displacement at 𝑡=2s.

Q2:

Given the velocity-time graph for a particle that moved in a straight line, determine its acceleration at 𝑡=3s.

Q3:

Given the velocity-time graph of a particle moving in a straight line, determine the displacement of the particle within the time interval [0,9].

Q4:

The figure shown is a velocity-time graph for two cars moving in a straight line. The movement of car 𝐴 is represented by the green line, and the movement of car 𝐵 by the blue line. Determine how long it took for the two cars to meet again, given that they started from the same point.

Q5:

The figure shown is a speed-time graph for a body moving in a straight line. Given that its initial speed was 5 m/s, determine the body’s acceleration during the part of the journey where the body was accelerating.

Q6:

The figure shown is a velocity-time graph for a body moving in a straight line. Determine the deceleration of the body during the final section of its movement, given that it came to rest 100 seconds after it started moving.

Q7:

Below is a velocity–time graph of a marathon runner running down a racetrack over a period of 8 seconds.

Find the acceleration of the runner during the first 2 seconds.

Find the distance covered by the runner over the 8-second period.

Q8:

The figure shows a velocity time graph of a particle moving in a straight line. When is the particle’s acceleration zero?

  • Afrom 𝑡=4 to 𝑡=6 and from 𝑡=10 to 𝑡=13
  • Bfrom 𝑡=4 to 𝑡=6
  • Cfrom 𝑡=1 to 𝑡=7
  • Dfrom 𝑡=10 to 𝑡=13

Q9:

Which color graph represents the path of a particle whose velocity is increasing?

  • AGreen
  • BBlue
  • CRed
  • DYellow

Q10:

Given the velocity-time graph of a particle moving in a straight line, determine the distance covered by the particle within the time interval [0,8].

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