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:

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].

Q5:

The given velocity-time graph represents a particle moving in a straight line. Determine its displacement at 𝑡=5s.

Q6:

Given the velocity-time graph of a particle moving in a straight line, determine the distance covered by the particle within the time interval [0,7].

Q7:

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

Q8:

Given the velocity-time graph of a particle moving in a straight line, determine the displacement of the particle within the time interval [0,7].

Q9:

Given the velocity-time graph of a particle moving in a straight line, determine the displacement of the particle within the time interval [0,6].

Q10:

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

Q11:

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.

Q12:

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.

Q13:

The figure shown is a velocity-time graph for a body moving in a straight line with an initial velocity of 10 m/s. Determine the total distance covered by the body, given that it came to rest 100 seconds after it started moving.

Q14:

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.

Q15:

Three cars, A, B, and C, are being driven along a straight road. The following graphs show how the velocity of each car changes once the driver sees that the traffic lights are red.

Which car stops in the shortest distance?

  • ACar B
  • BCar C
  • CCar A

Q16:

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.

Q17:

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

Q18:

Daniel made a 60-minute trip to town. The given graph shows the distance he was from his house throughout his trip.

He stopped at two shops. At what times was that?

  • A20≤𝑡≤27 and 40≤𝑡≤49
  • B10≤𝑡≤20 and 50≤𝑡≤60
  • C16≤𝑡≤33 and 49≤𝑡≤60
  • D16≤𝑡≤26 and 44≤𝑡≤49
  • E0≤𝑡≤16 and 33≤𝑡≤43

At some point, he changed direction without stopping first. When was that?

  • A𝑡=32
  • B𝑡=43
  • C𝑡=20
  • D𝑡=27
  • E𝑡=50

At what times was he moving toward his house?

  • A10≤𝑡≤20 and 50≤𝑡≤60
  • B26≤𝑡≤32 and 49≤𝑡≤60
  • C0≤𝑡≤16 and 33≤𝑡≤43
  • D20≤𝑡≤27 and 40≤𝑡≤49
  • E16≤𝑡≤33 and 49≤𝑡≤60

At which minute was he moving fastest?

  • A𝑡=50
  • B𝑡=33
  • C𝑡=43
  • D𝑡=27
  • E𝑡=55

Q19:

The figure shows a velocity-time graph for a car moving in a straight line. Given that 𝑣 is measured in metres per second and 𝑡 in seconds, determine when the car is moving forward.

  • Afrom 𝑡=0s to 𝑡=3s and from 𝑡=8s to 𝑡=11s
  • Bfrom 𝑡=5s to 𝑡=8s
  • Cfrom 𝑡=0s to 𝑡=2s and from 𝑡=6s to 𝑡=11s
  • Dfrom 𝑡=0s to 𝑡=3s

Q20:

The three graphs in the figure show the position of a particle, its velocity, and its acceleration against time, respectively. Identify each graph.

  • ADisplacement–time graph: red, velocity–time graph: blue, acceleration–time graph: green
  • BDisplacement–time graph: blue, velocity–time graph: red, acceleration–time graph: green
  • CDisplacement–time graph: red, velocity–time graph: green, acceleration–time graph: blue
  • DDisplacement–time graph: green, velocity–time graph: blue, acceleration–time graph: red
  • EDisplacement–time graph: green, velocity–time graph: red, acceleration–time graph: blue

Q21:

The figure shows a velocity-time graph for a particle moving in a straight line. When is the acceleration of the particle negative?

  • Afrom 𝑡=6 to 𝑡=9
  • Bfrom 𝑡=0 to 𝑡=4 and from 𝑡=9 to 𝑡=11
  • Cfrom 𝑡=0 to 𝑡=3, from 𝑡=6 to 𝑡=8, and from 𝑡=9 to 𝑡=11
  • Dfrom 𝑡=4 to 𝑡=6 and from 𝑡=11 to 𝑡=13

Q22:

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

  • AGreen
  • BBlue
  • CRed
  • DYellow

Q23:

Which color graph represents the path of a particle with uniform acceleration?

  • AGraph D
  • BGraph B
  • CGraph A
  • DGraph C

Q24:

The following figure shows a velocity time–graph of a particle moving in a straight line.

When is the particle moving backward?

  • A[9,13]
  • B[2,3]∪[9,10]
  • C[3,10]
  • D[3,6]
  • E[10,13]

When is the particle moving at a constant velocity?

  • A[10,13]
  • B[3,6]
  • C[2,3]∪[9,10]
  • D[3,10]
  • E[0,2]∪[6,9]

Q25:

True or False: In a velocity–time graph, if, at a given time, the graph has a negative slope, then the object has positive acceleration at that time.

  • ATrue
  • BFalse

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