Worksheet: Finding Momentum Using Differentiation or Integration

In this worksheet, we will practice calculating the momentum of a particle of mass m moving in a straight line with velocity v by using integration or differentiation.

Q1:

A body of mass 5 kg moves in a straight line such that, at time 𝑑 seconds, its displacement from a fixed point on the line is given by 𝑠 = [ 2 𝑑 ( 9 βˆ’ 3 𝑑 ) ] , 𝑑 β‰₯ 0 m . Calculate the magnitude of the change in its momentum in the first 2 seconds.

Q2:

A car of mass 1,350 kg moves in a straight line such that at time 𝑑 seconds, its displacement from a fixed point on the line is given by 𝑠 = ο€Ή 6 𝑑 βˆ’ 3 𝑑 + 4   m . Find the magnitude of the car’s momentum at 𝑑 = 3 s .

Q3:

A body of mass π‘š is moving in a straight line. At time 𝑑 seconds, where 𝑑 β‰₯ 0 , the body’s displacement relative to a fixed point is given by ⃑ 𝑠 =  ( 2 𝑑 ) ⃑ 𝑖 βˆ’ ( 6 𝑑 ) ⃑ 𝑗  m , where ⃑ 𝑖 and ⃑ 𝑗 are perpendicular unit vectors. Given that the body’s kinetic energy is 660 joules, determine the magnitude of its momentum.

  • A 2 0 √ 3 3 kgβ‹…m/s
  • B 1 320 kgβ‹…m/s
  • C 660 kgβ‹…m/s
  • D 6 6 √ 1 0 kgβ‹…m/s

Q4:

A body of mass 5 kg moves along a straight line. At time 𝑑 seconds, its acceleration is given by π‘Ž = ( βˆ’ 6 𝑑 βˆ’ 8 ) m / s  . Find the change in its momentum in the time interval 6 ≀ 𝑑 ≀ 9 .

Q5:

A body of mass 8 kg moves along a straight line. At time 𝑑 seconds, its acceleration is given by π‘Ž = ( 1 0 𝑑 + 5 ) m / s  . Find the change in its momentum in the time interval 4 ≀ 𝑑 ≀ 1 2 .

Q6:

A body of mass 8 kg moves along a straight line. At time 𝑑 seconds, its acceleration is given by π‘Ž = ( 5 𝑑 + 3 ) m / s  . Find the change in its momentum in the time interval 1 2 ≀ 𝑑 ≀ 1 4 .

Q7:

A body of mass 4 kg moves in a straight line such that, at time 𝑑 seconds, its displacement from a fixed point on the line is given by 𝑠 = [ 3 𝑑 ( 9 βˆ’ 3 𝑑 ) ] , 𝑑 β‰₯ 0 m . Calculate the magnitude of the change in its momentum in the first 2 seconds.

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