5 A car of mass 900 kg moves along a straight level road. The power developed by the car is constant and equal to 60 kW . The resistance to the motion of the car is constant and equal to 1500 N .
At time \(t\) seconds the velocity of the car is denoted by \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Initially the car is at rest.
- Show that \(\frac { 3 v } { 5 } \frac { \mathrm {~d} v } { \mathrm {~d} t } = 40 - v\).
- Verify that \(t = 24 \ln \left( \frac { 40 } { 40 - v } \right) - \frac { 3 } { 5 } v\).