- A car of mass 600 kg is moving along a straight horizontal road.
At the instant when the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the resistance to the motion of the car is modelled as a force of magnitude \(( 200 + 2 v ) \mathrm { N }\).
The engine of the car is working at a constant rate of 12 kW .
- Find the acceleration of the car at the instant when \(v = 20\)
Later on the car is moving up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 14 }\)
At the instant when the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the resistance to the motion of the car from non-gravitational forces is modelled as a force of magnitude ( \(200 + 2 v ) \mathrm { N }\).
The engine is again working at a constant rate of 12 kW .
At the instant when the car has speed \(w \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the car is decelerating at \(0.05 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). - Find the value of \(w\).