A battery–powered mini-car of unknown mass starts from rest on a level track

PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power

Problem

A battery–powered mini-car of unknown mass

m

starts from rest on a level track. Its electric motor delivers a constant power output of

12\,\text{kW}

for

10\,\text{s}

. Assume that all the power supplied by the motor goes into increasing the kinetic energy of the car and that frictional losses are negligible. (i) Write an equation relating the work done by the motor, its power output, and the time for which it operates. (ii) Using your result from part (i), derive an expression for the mass

m

of the car in terms of the power

P

, the operating time

t

, and the final speed

v

attained at

t=10\,\text{s}

. (iii) The speed measured at

t=10\,\text{s}

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

. Calculate the mass of the car. (iv) If the designers wish the same motor (still

12\,\text{kW}

) to accelerate a lighter prototype to

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

in the same time of

10\,\text{s}

, what should be the maximum mass of the prototype? Comment briefly on the practicality of achieving such a reduction.

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