- A particle \(P\) of mass 0.5 kg moves on the \(x\)-axis under the action of a single force.
At time \(t\) seconds, \(t \geqslant 0\)
- \(O P = x\) metres, \(0 \leqslant x < \frac { \pi } { 2 }\)
- the force has magnitude \(\sin 2 x \mathrm {~N}\) and is directed towards the origin \(O\)
- \(P\) is moving in the positive \(x\) direction with speed \(v \mathrm {~ms} ^ { - 1 }\)
At time \(t = 0 , P\) passes through the origin with speed \(2 \mathrm {~ms} ^ { - 1 }\)
- Show that \(v = 2 \cos x\)
- Show that \(t = \frac { 1 } { 2 } \ln ( \sqrt { 2 } + 1 )\) when \(x = \frac { \pi } { 4 }\)