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 seconds, its displacement from a fixed point on the line is given by . 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 seconds, its displacement from a fixed point on the line is given by . Find the magnitude of the car’s momentum at .

Q3:

A body of mass is moving in a straight line. At time seconds, where , the body’s displacement relative to a fixed point is given by , where and are perpendicular unit vectors. Given that the body’s kinetic energy is 660 joules, determine the magnitude of its momentum.

• A kg⋅m/s
• B 1 320 kg⋅m/s
• C 660 kg⋅m/s
• D kg⋅m/s

Q4:

A body of mass 5 kg moves along a straight line. At time seconds, its acceleration is given by . Find the change in its momentum in the time interval .

Q5:

A body of mass 8 kg moves along a straight line. At time seconds, its acceleration is given by . Find the change in its momentum in the time interval .

Q6:

A body of mass 8 kg moves along a straight line. At time seconds, its acceleration is given by . Find the change in its momentum in the time interval .

Q7:

A body of mass 4 kg moves in a straight line such that, at time seconds, its displacement from a fixed point on the line is given by . Calculate the magnitude of the change in its momentum in the first 2 seconds.