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In this lesson, we will learn how to calculate 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 along a straight line. At time π‘ seconds, its acceleration is given by π = ( β 6 π‘ β 8 ) / m s 2 . Find the change in its momentum in the time interval 6 β€ π‘ β€ 9 .

Q2:

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

Q3:

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

Q4:

A car of mass 1β350 kg moves in a straight line such that at time π‘ seconds, its displacement from a fixed point on the line is given by π = οΉ 6 π‘ β 3 π‘ + 4 ο 2 m . Find the magnitude of the carβs momentum at π‘ = 3 s .

Q5:

A body of mass π is moving in a straight line. At time π‘ seconds, where π‘ β₯ 0 , the bodyβs displacement relative to a fixed point is given by β π = ο ( 2 π‘ ) β π β ( 6 π‘ ) β π ο m , where β π and β π are perpendicular unit vectors. Given that the bodyβs kinetic energy is 660 joules, determine the magnitude of its momentum.

Q6:

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

Q7:

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

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