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June 2016 p41 q3
3444
A car of mass 1000 kg is moving along a straight horizontal road against resistances of total magnitude 300 N.
(i) Find, in kW, the rate at which the engine of the car is working when the car has a constant speed of 40 m s-1.
(ii) Find the acceleration of the car when its speed is 25 m s-1 and the engine is working at 90% of the power found in part (i).
Solution
(i) The driving force required to overcome the resistance is 300 N. The power \(P\) is given by the formula \(P = Fv\), where \(F\) is the force and \(v\) is the velocity.
Substituting the given values, \(P = 300 \times 40 = 12000 \text{ W} = 12 \text{ kW}\).
(ii) The power at 90% of the value found in part (i) is \(0.9 \times 12000 = 10800 \text{ W}\).
Using the formula \(P = Fv\), we find the driving force \(F\) when the speed is 25 m s-1: \(F = \frac{10800}{25} = 432 \text{ N}\).
Applying Newton's second law, \(F - 300 = 1000a\), where 300 N is the resistance.
Thus, \(432 - 300 = 1000a\).
Solving for \(a\), we get \(a = \frac{132}{1000} = 0.132 \text{ ms}^{-2}\).