- A particle of mass 2 kg is moving in a straight line on a smooth horizontal surface under the action of a horizontal force of magnitude \(F\) newtons.
At time \(t\) seconds \(( t > 0 )\),
- the particle is moving with speed \(v \mathrm {~ms} ^ { - 1 }\)
- \(F = 2 + v\)
The time taken for the speed of the particle to increase from \(5 \mathrm {~ms} ^ { - 1 }\) to \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is \(T\) seconds.
- Show that \(T = 2 \ln \frac { 12 } { 7 }\)
The distance moved by the particle as its speed increases from \(5 \mathrm {~ms} ^ { - 1 }\) to \(10 \mathrm {~ms} ^ { - 1 }\) is \(D\) metres.
- Find the exact value of \(D\).