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Worksheet: Linear Motion Described Using Differentiation

Q1:

A particle is moving in a straight line such that its displacement after seconds is given by Determine the time interval during which the velocity of the particle is increasing.

  • A
  • B
  • C
  • D

Q2:

A particle moves in a straight line such that at time 𝑡 seconds its displacement from a fixed point on the line is given by Determine whether the particle is accelerating or decelerating when 𝑡 = 2 s .

  • Aaccelerating
  • Bdecelerating

Q3:

A particle started moving along the 𝑥 -axis. When the particle’s displacement from the origin is 𝑥 meters, its velocity is given by Find the particle’s acceleration when its velocity vanished.

  • A 3 m/s2
  • B 7 m/s2
  • C 2 m/s2
  • D 6 m/s2
  • E 4 m/s2

Q4:

A particle moves along the -axis such that at time seconds ( ) its velocity is given by . Determine the time interval in which the particle decelerates.

  • A
  • B
  • C
  • D
  • E

Q5:

A particle is moving in a straight line such that its displacement after 𝑡 seconds is given by When the particle’s velocity is zero, its acceleration is 𝑎 m/s2. Find all the possible values of 𝑎 .

  • A24, 22
  • B27, 25
  • C12, 10
  • D 1 2 , 12

Q6:

A particle moves along the 𝑥 -axis. At time 𝑡 seconds, its displacement from the origin is given by Determine the time at which the particle’s acceleration is 9 m/s2.

  • A 1 5 7 s
  • B 3 s
  • C 4 1 2 s
  • D 1 1 2 s
  • E 2 1 2 s

Q7:

A particle is moving in a straight line such that its displacement 𝑠 at 𝑡 seconds is given by Find the velocity of the particle when the acceleration is zero.

Q8:

A particle is moving in a straight line such that its displacement 𝑠 in meters is given as a function of time 𝑡 in seconds by Find the magnitude of the acceleration of the particle when the velocity is zero.

  • A 195 m/s2
  • B 498 m/s2
  • C 81 m/s2
  • D 162 m/s2

Q9:

A particle moves along the 𝑥 -axis such that at time 𝑡 seconds, its displacement from the origin is given by What is the particle’s average velocity in the first 10 seconds?

Q10:

A particle is moving in a straight line such that its position 𝑟 meters relative to the origin at time 𝑡 seconds is given by Find the particle’s average velocity between 𝑡 = 2 s and 𝑡 = 4 s .

  • A 18 m/s
  • B 11 m/s
  • C 2 m/s
  • D 9 m/s

Q11:

A particle moves along the 𝑥 -axis. When its displacement from the origin is 𝑠 m, its velocity is given by Find the particle’s acceleration when 𝑠 = 3 m .

  • A 1 9 m/s2
  • B 4 9 m/s2
  • C 4 9 m/s2
  • D 2 2 7 m/s2
  • E 1 6 m/s2

Q12:

A particle started moving along the -axis. At time seconds, the its displacement from the origin is given by Find the body’s average speed within the time interval .

Q13:

A body moves along the 𝑥 -axis such that at time 𝑡 seconds, its displacement from the origin is given by What is its velocity when its acceleration is equal to 0?

  • A 1 4 9 m/s
  • B 3 2 m/s
  • C 8 1 5 m/s
  • D 2 2 9 m/s