A particle \(P\) moves on the \(x\)-axis. At time \(t\) seconds, its acceleration is \(( 5 - 2 t ) \mathrm { m } \mathrm { s } ^ { - 2 }\), measured in the direction of \(x\) increasing. When \(t = 0\), its velocity is \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) measured in the direction of \(x\) increasing. Find the time when \(P\) is instantaneously at rest in the subsequent motion.
A car of mass 1200 kg moves along a straight horizontal road with a constant speed of \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The resistance to motion of the car has magnitude 600 N .
Find, in kW , the rate at which the engine of the car is working.
The car now moves up a hill inclined at \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 28 }\). The resistance to motion of the car from non-gravitational forces remains of magnitude 600 N . The engine of the car now works at a rate of 30 kW .
Find the acceleration of the car when its speed is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).