3. A body, of mass 9 kg , is projected along a straight horizontal track with an initial speed of \(20 \mathrm {~ms} ^ { - 1 }\). At time \(t \mathrm {~s}\) the body experiences a resistance of magnitude \(( 0.2 + 0.03 v ) \mathrm { N }\) where \(v \mathrm {~ms} ^ { - 1 }\) is its speed.

1. Show that \(v\) satisfies the differential equation $$900 \frac { \mathrm {~d} v } { \mathrm {~d} t } = - ( 20 + 3 v )$$
2. Find an expression for \(t\) in terms of \(v\).
3. Calculate, to the nearest second, the time taken for the body to come to rest.