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Lesson: Linear Motion Described Using Differentiation

Sample Question Videos

Worksheet • 13 Questions • 1 Video

Q1:

A particle is moving in a straight line such that its displacement ๐‘  after ๐‘ก seconds is given by Determine the time interval during which the velocity of the particle is increasing.

  • A ] 6 , โˆž [
  • B ] 1 2 , โˆž [
  • C ] 3 6 , โˆž [
  • D ] 1 8 , โˆž [

Q2:

A particle moves in a straight line such that at time ๐‘ก seconds its displacement from a fixed point on the line is given by Determine whether the particle is accelerating or decelerating when ๐‘ก = 2 s .

  • Adecelerating
  • Baccelerating

Q3:

A particle started moving along the ๐‘ฅ -axis. When the particleโ€™s displacement from the origin is ๐‘ฅ metres, its velocity is given by Find the particleโ€™s acceleration when its velocity vanished.

Q4:

A particle moves along the ๐‘ฅ -axis such that at time seconds ( ๐‘ก โ‰ฅ 0 ) its velocity is given by ๐‘ฃ = ( 3 ๐‘ก โˆ’ 9 ๐‘ก ) / 2 m s . Determine the time interval in which the particle decelerates.

  • A ๏  3 2 , 3 ๏”
  • B ๏  โˆ’ โˆž , 3 2 ๏”
  • C ] 0 , 3 ]
  • D ] 3 , โˆž [
  • E ๏  0 , 3 2 ๏”

Q5:

A particle is moving in a straight line such that its displacement after ๐‘ก seconds is given by When the particleโ€™s velocity is zero, its acceleration is ๐‘Ž m/s2. Find all the possible values of ๐‘Ž .

  • A โˆ’ 1 2 , 12
  • B27, 25
  • C12, 10
  • D24, 22

Q6:

A particle moves along the ๐‘ฅ -axis. At time ๐‘ก seconds, its displacement from the origin is given by Determine the time at which the particleโ€™s acceleration is 9 m/s2.

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

Q7:

A particle is moving in a straight line such that its displacement ๐‘  at ๐‘ก 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 ๐‘  in metres is given as a function of time ๐‘ก in seconds by Find the magnitude of the acceleration of the particle when the velocity is zero.

Q9:

A particle moves along the ๐‘ฅ -axis such that at time ๐‘ก seconds, its displacement from the origin is given by What is the particleโ€™s average velocity in the first 10 seconds?

Q10:

A particle is moving in a straight line such that its position ๐‘Ÿ meters relative to the origin at time ๐‘ก seconds is given by Find the particleโ€™s average velocity between ๐‘ก = 2 s and ๐‘ก = 4 s .

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

Q11:

A particle moves along the ๐‘ฅ -axis. When its displacement from the origin is ๐‘  m, its velocity is given by Find the particleโ€™s acceleration when ๐‘  = 3 m .

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

Q12:

A particle started moving along the ๐‘ฅ -axis. At time ๐‘ก seconds, the its displacement from the origin is given by Find the bodyโ€™s average speed within the time interval [ 0 , 5 ] .

Q13:

A body moves along the ๐‘ฅ -axis such that at time ๐‘ก seconds, its displacement from the origin is given by What is its velocity when its acceleration is equal to 0?

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