6 A stone of mass 0.125 kg falls freely under gravity, from rest, until it has travelled a distance of 10 m . The stone then continues to fall in a medium which exerts an upward resisting force of \(0.025 v \mathrm {~N}\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed of the stone \(t \mathrm {~s}\) after the instant that it enters the resisting medium.

1. Show by integration that \(v = 49 - 35 \mathrm { e } ^ { - 0.2 t }\).
2. Find how far the stone travels during the first 3 seconds in the medium.