A 1 000-kg sports car accelerates from zero to 25 m/s in 7.0 s.What is the average power delivered by the automobile engine?
A)8.9E+4 W
B)1.8E+3 W
C)4.5E+4 W
D)1.8E+5 W
E)5.4E+4 W

Question

Quizplus · Accepted Answer

The work done on the car during acceleration is given by the kinetic energy gained:

KE = (1/2)mv^2 - (1/2)mv_0^2

where m = 1000 kg is the mass of the car, v = 25 m/s is the final velocity, and v_0 = 0 is the initial velocity. Plugging in the numbers, we get:

KE = (1/2)(1000 kg)(25 m/s)^2 = 312500 J

The time interval for acceleration is Δt = 7.0 s. The average power delivered by the engine is given by:

P = ΔKE/Δt

Plugging in the numbers, we get:

P = 312500 J/7.0 s = 44643 W ≈ 4.5 × 10^4 W

Therefore, the best choice is C.

A 1 000-Kg Sports Car Accelerates from Zero to 25