Lesson Worksheet: Displacement–Time Graphs Mathematics

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In this worksheet, we will practice using displacement–time graphs and interpret the slope of the curve as the velocity of the body.

Q1:

This displacement–time graph shows the journey of a car along a straight road. The journey has four stages: 𝐴, 𝐵, 𝐶, and 𝐷.

Calculate the average velocity for each stage of the journey.

  • A𝐴=80/kmh, 𝐵=0/kmh, 𝐶=80/kmh, 𝐷=40/kmh
  • B𝐴=0/kmh, 𝐵=80/kmh, 𝐶=40/kmh, 𝐷=−40/kmh
  • C𝐴=80/kmh, 𝐵=0/kmh, 𝐶=80/kmh, 𝐷=−40/kmh
  • D𝐴=80/kmh, 𝐵=0/kmh, 𝐶=40/kmh, 𝐷=40/kmh
  • E𝐴=80/kmh, 𝐵=0/kmh, 𝐶=40/kmh, 𝐷=−40/kmh

Write down the average velocity for the whole journey.

Calculate the average speed for the whole journey.

Q2:

This displacement–time graph shows the journey of a cyclist along a straight road. She cycles in a straight line for 15 minutes and then stops for 10 minutes. Finally, she cycles back to her starting point in 25 minutes, traveling in a straight line.

Calculate the average velocity for each stage of the journey in kilometers per hour.

  • A0.26 km/h, 0 km/h, −9.6 km/h
  • B16 km/h, 0 km/h, −9.6 km/h
  • C0.26 km/h, 0 km/h, −0.16 km/h
  • D16 km/h, 0 km/h, −0.16 km/h
  • E16 km/h, 0 km/h, 9.6 km/h

Q3:

This displacement–time graph shows the motion of a particle in a straight line. It travels away from its starting point for 15 minutes and then returns in 30 minutes.

Calculate the average speed for the whole journey in kilometers per hour.

Calculate the average velocity for the whole journey in kilometers per hour.

Q4:

The position-time graph given below describes an object’s motion.

Which of the following statements is true?

  • AThevelocityispositiveatand𝑡=4𝑡=24.
  • BThevelocityispositiveatthetimeintervalonly16<𝑡<24.
  • CThevelocityispositiveatthetimeintervalsand0<𝑡<816<𝑡<24.
  • DThevelocityispositiveatand𝑡=3𝑡=16.
  • EThevelocityispositiveatthetimeintervalonly0<𝑡<8.

Q5:

The displacement-time graph given below describes the motion of an object.

At what time is the object at rest (velocity = zero)?

  • A𝑡=3
  • B𝑡=4
  • C𝑡=0.75
  • D𝑡=2
  • E2<𝑡<3

Q6:

The horizontal position of an object in meters over time is shown in the following displacement–time graph. Find the value of the velocity at 𝑡=1 s.

  • A−23 m/s
  • B12 m/s
  • C23 m/s
  • D1 m/s
  • E32 m/s

Q7:

This is the displacement–time graph for a ball that is thrown vertically up in the air and falls back down to its starting point.

Find the maximum height reached by the ball.

Find the time at which the ball reaches its maximum height.

Q8:

A ball is thrown vertically up in the air and falls back to the ground. Its displacement–time graph is shown below.

Write down the velocity of the ball when it reaches its maximum height.

Q9:

This displacement-time graph describes an object’s motion.

Which of the following statements is true?

  • AThevelocityispositiveatthetimeintervalonly3<𝑡<4.
  • BThevelocityispositiveatthetimeintervalsand0<𝑡<13<𝑡<4.
  • CThevelocityispositiveatthetimeintervalonly0<𝑡<1.
  • DThevelocityispositiveatthetimeinterval0<𝑡<2.
  • EThevelocityispositiveatthetimeinterval1<𝑡<3.

Q10:

A motorcycle was moving uniformly such that, after 4 minutes, it was 25 km away from a certain point and, after 8 minutes, it was 29 km away from the same point. Determine the relation between the distance from that point 𝑠 measured in meters and the time 𝑡 measured in minutes.

  • A𝑠=21𝑡+1
  • B𝑠=7𝑡+4.5
  • C𝑠=4.5𝑡+7
  • D𝑠=𝑡+21

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