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Lesson: Rectilinear Motion with Integrals

In this lesson, we will learn how to use definite integrals to solve problems involving rectilinear motion.

Sample Question Videos

01:29

Worksheet • 10 Questions • 1 Video

Q1:

A car, starting from rest, began moving in a straight line from a fixed point. Its velocity after 𝑑 seconds is given by Calculate the displacement of the car when 𝑑 = 9 s e c o n d s .

Q2:

A particle accelerates at the rate of 2 𝑑 + 7 m/s2 after 𝑑 seconds of motion. If 𝑣 ( 0 ) = βˆ’ 8 m/s, how long does it take for the velocity to reach 50 m/s? Give your answer to 2 decimal places.

Q3:

If 𝑓 ( 𝑑 ) = 𝐹 ( 𝑑 ) β€² is the velocity of a particle in motion, in kilometres per hour, what is the unit of ο„Έ 𝑓 ( 𝑑 ) 𝑑 𝑏 π‘Ž d ?

  • A kilometres
  • B kilometres per hour
  • C hours per kilometre
  • D hours

Q4:

A particle is moving in a straight line such that its acceleration at time 𝑑 seconds is given by Given that its initial velocity is 20 m/s, find an expression for its displacement in terms of 𝑑 .

  • A ο€Ύ 𝑑 3 βˆ’ 9 𝑑 + 2 0 𝑑  3 2 m
  • B ο€Ή 𝑑 βˆ’ 1 8 𝑑 + 2 0  2 m
  • C ο€Ή 𝑑 βˆ’ 1 8 𝑑  2 m
  • D ο€Ή 𝑑 βˆ’ 2 7 𝑑  3 2 m

Q5:

A particle moves along the π‘₯ -axis. At time 𝑑 seconds, its acceleration is given by Given that at 𝑑 = 2 s , its velocity is 28 m/s, what is its initial velocity?

Q6:

A particle is moving in a straight line such that its velocity at time 𝑑 seconds is given by Given that its initial position from a fixed point is 20 m, find an expression for its displacement at time 𝑑 seconds.

  • A ο€Ή 5 𝑑 βˆ’ 4 𝑑 + 2 0  3 2 m
  • B ( 3 0 𝑑 βˆ’ 8 ) m
  • C ( 3 0 𝑑 + 2 0 ) m
  • D ο€Ή 5 𝑑 βˆ’ 8 𝑑 + 2 0  3 2 m

Q7:

A particle is moving in a straight line such that its velocity at time 𝑑 seconds is given by Given that its initial position from a fixed point is 4 m, find an expression for its displacement at time 𝑑 seconds.

  • A ο€Ύ 5 𝑑 3 βˆ’ 𝑑 2 + 4  3 2 m
  • B ( 1 0 𝑑 βˆ’ 1 ) m
  • C ( 1 0 𝑑 + 4 ) m
  • D ο€Ύ 5 𝑑 3 βˆ’ 𝑑 + 4  3 2 m

Q8:

The figure shows a velocity-time graph for a particle moving in a straight line. Find the total distance the particle travelled.

Q9:

The figure shows a velocity-time graph for a particle moving in a straight line. Find the total distance the particle travelled.

Q10:

A particle moves along the positive π‘₯ axis, starting at π‘₯ = 1 m . It’s acceleration varies directly with 𝑑 2 , where 𝑑 is the time in seconds. At 𝑑 = 1 s , the particle’s displacement is 12 m, and its velocity is 14 m/s. Express the particle’s displacement, 𝑠 , and its velocity, 𝑣 , in terms of 𝑑 .

  • A 𝑣 = ο€Ή 4 𝑑 + 1 0  / 3 m s , 𝑠 = ο€Ή 𝑑 + 1 0 𝑑 + 1  4 m
  • B 𝑣 = ο€Ή 6 𝑑 + 1 0  / 3 m s , 𝑠 = ο€Ή 𝑑 + 1 0 𝑑 + 1  4 m
  • C 𝑣 = ο€Ύ 1 0 0 𝑑 3 βˆ’ 5 8 3  / 3 m s , 𝑠 = ο€Ύ 2 5 𝑑 3 βˆ’ 5 8 𝑑 3 + 1  4 m
  • D 𝑣 = ο€Ή 6 𝑑 + 1 0  / 3 m s , 𝑠 = ο€Ή 𝑑 + 1 0 𝑑 βˆ’ 1  4 m
  • E 𝑣 = ο€Ό 5 0 𝑑 βˆ’ 5 8 3  / 3 m s , 𝑠 = ο€Ύ 2 5 𝑑 3 βˆ’ 5 8 𝑑 3 + 1  4 m
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