A ship \(S\) is moving with constant velocity \(( 4 \mathbf { i } - 7 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors due east and due north respectively.
Find the speed and direction of \(S\), giving the direction as a three-figure bearing, correct to the nearest degree.
The diagram below shows a forklift truck being used to raise two boxes, \(P\) and \(Q\), vertically. Box \(Q\) rests on horizontal forks and box \(P\) rests on top of box \(Q\). Box \(P\) has mass 25 kg and box \(Q\) has mass 55 kg .
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When the boxes are moving upwards with uniform acceleration, the reaction of the horizontal forks on box \(Q\) is 820 N . Calculate the magnitude of the acceleration.
Calculate the reaction of box \(Q\) on box \(P\) when they are moving vertically upwards with constant speed.
A particle, of mass 4 kg , moves in a straight line under the action of a single force \(F \mathrm {~N}\), whose magnitude at time \(t\) seconds is given by
$$F = 12 \sqrt { t } - 32 \text { for } t \geqslant 0 .$$
Find the acceleration of the particle when \(t = 9\).
Given that the particle has velocity \(- 1 \mathrm {~ms} ^ { - 1 }\) when \(t = 4\), find an expression for the velocity of the particle at \(t \mathrm {~s}\).
Determine whether the speed of the particle is increasing or decreasing when \(t = 9\). [2]