Energy method - horizontal motion with resistance (no driving force)

3 A particle of mass 1.2 kg moves in a straight line \(A B\). It is projected with speed \(7.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from \(A\) towards \(B\) and experiences a resistance force. The work done against this resistance force in moving from \(A\) to \(B\) is 25 J .

1. Given that \(A B\) is horizontal, find the speed of the particle at \(B\).
2. It is given instead that \(A B\) is inclined at \(30 ^ { \circ }\) below the horizontal and that the speed of the particle at \(B\) is \(9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The work done against the resistance force remains the same. Find the distance \(A B\).

A particle of mass 4 kg is moving in a straight horizontal line. There is a constant resistive force of magnitude \(R\) newtons. The speed of the particle is reduced from 25 m s\(^{-1}\) to rest over a distance of 200 m. Use the work-energy principle to calculate the value of \(R\). [4]

A parcel of mass 2.5 kg is moving in a straight line on a smooth horizontal floor. Initially the parcel is moving with speed 8 m s\(^{-1}\). The parcel is brought to rest in a distance of 20 m by a constant horizontal force of magnitude \(R\) newtons. Modelling the parcel as a particle, find

1. the kinetic energy lost by the parcel in coming to rest, [2]
2. the value of \(R\). [3]