A 2000 kg car accelerates from rest to a velocity of 20 m/s in 10 seconds. The average power of the engine during this acceleration is
A) 50 kW.
B) 40 kW.
C) 30 kW.
D) 20 kW.
E) 10 kW.

Question

Quizplus · Accepted Answer

The average power can be calculated using the formula for power, which is the work done over time, $P = \frac{W}{t}$. The work done on the car is equal to the change in kinetic energy, $W = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mu^2$, where $m$ is the mass, $v$ is the final velocity, and $u$ is the initial velocity. Given that the car accelerates from rest ($u = 0$) to $v = 20$ m/s, the change in kinetic energy is $\Delta KE = \frac{1}{2} \times 2000 \times 20^2 = 400,000$ Joules. The time taken is 10 seconds, so the average power is $P = \frac{400,000}{10} = 40,000$ Watts or 40 kW.

A 2000 Kg Car Accelerates from Rest to a Velocity