A caravan of mass 600 kg is towed by a car of mass 900 kg along a straight horizontal road. The towbar joining the car to the caravan is modelled as a light rod parallel to the road. The total resistance to motion of the car is modelled as having magnitude 300 N . The total resistance to motion of the caravan is modelled as having magnitude 150 N . At a given instant the car and the caravan are moving with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and acceleration \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
Find the power being developed by the car's engine at this instant.
Find the tension in the towbar at this instant.
A ball of mass 0.2 kg is projected vertically upwards from a point \(O\) with speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The non-gravitational resistance acting on the ball is modelled as a force of constant magnitude 1.24 N and the ball is modelled as a particle. Find, using the work-energy principle, the speed of the ball when it first reaches the point which is 8 m vertically above \(O\).
(6)
A particle \(P\) moves along a straight line in such a way that at time \(t\) seconds its velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is given by
$$v = \frac { 1 } { 2 } t ^ { 2 } - 3 t + 4$$
Find
the times when \(P\) is at rest,
the total distance travelled by \(P\) between \(t = 0\) and \(t = 4\).