5. A car, of mass 1100 kg , pulls a trailer of mass 550 kg along a straight horizontal road by means of a rigid tow-bar. The car is accelerating at \(1.2 \mathrm {~ms} ^ { - 2 }\) and the resistances to the motion of the car and trailer have magnitudes 500 N and 200 N respectively.
- Show that the driving force produced by the engine of the car is 2680 N .
- Find the tension in the tow-bar between the car and the trailer.
- Find the rate, in kW , at which the car's engine is working when the car is moving with speed \(18 \mathrm {~ms} ^ { - 1 }\).
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When the car is moving at \(18 \mathrm {~ms} ^ { - 1 }\) it starts to climb a straight hill which is inclined at \(6 ^ { \circ }\) to the horizontal. If the car's engine continues to work at the same rate and the resistances to motion remain the same as previously, - find the acceleration of the car at the instant when it starts to climb the hill.
- Show that tension in the tow-bar remains unchanged.