A car of mass is travelling at on a level track

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A car of mass

1000\,\text{kg}

is travelling at

5.0\,\text{m\,s}^{-1}

on a level track. At that instant the throttle is fully opened so that the engine thereafter supplies a constant power of

20\,\text{kW}

. External resistance forces are negligible. (i) Derive an expression for the speed

v

of the car as a function of time

t

measured from the instant the power becomes

20\,\text{kW}

. (ii) Using the expression obtained in part (i), calculate the time taken for the speed to rise from

5.0\,\text{m\,s}^{-1}

10.0\,\text{m\,s}^{-1}

. (iii) Find the distance travelled by the car during the interval calculated in part (ii).