Question

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

• A. B
• B. A
• C. Both exert same power
• D. Data insufficient

Answer 1

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$u_1=10m{s}^{-1}$
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 $u_2=5m{s}^{-1}$
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 $P_1=\frac{250}{10}=25J{s}^{-1}$
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 $P_2$​ = $\frac{125}{10}=12.5J{s}^{-1}$
Hence A exerts more power than B.