Two cars A and B with a mass of 5 kg and 10 kg and initial velocities of $10 m s^{- 1}$ and $5 m s^{- 1}$ are racing. Which car exerts more power before coming to rest? (Time taken for both cars to complete the race is 10 seconds):

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Both exert same power

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Data insufficient

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Solution

The correct option is B. A
Let $W_{1}$ be the work done and $P_{1}$ be the power exerted by car A.
Let $W_{2}$ be the work done and $P_{2}$ be the power exerted by car B.
Given mass of car A, $m_{1}$ = 5 kg
initial velocity of car A $u_{1} = 10 m s^{- 1}$
final velocity of car A, $v_{1} = 0$ (since the car comes to rest)
mass of car B, $m_{2}$ = 10 kg
initial velocity of car B $u_{2} = 5 m s^{- 1}$
final velocity of car B, $v_{2} = 0$ (since the car comes to rest)
Since work done = change in kinetic energy
work done by car A = final K.E - initial K.E = $\frac{m v_{1}^{2}}{2} - \frac{m u_{1}^{2}}{2} = 0 - \frac{m u_{1}^{2}}{2}$
$W_{1}$ = $\frac{1}{2} \times m_{1} \times {u_{1}}^{2} = 0.5 \times 5 \times 100 = 250$ ,
So $P_{1} = \frac{250}{10} = 25 J s^{- 1}$
work done by car B = final K.E - initial K.E = $\frac{m v_{1}^{2}}{2} - \frac{m u_{1}^{2}}{2} = 0 - \frac{m u_{2}^{2}}{2}$
$W_{2}$ = $\frac{1}{2} \times m_{2} \times {u_{2}}^{2} = 0.5 \times$ 10 $\times$ 25 = 125, So $P_{2}$ = $\frac{125}{10} = 12.5 J s^{- 1}$
Hence A exerts more power than B.

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