A 1.73e+03 kg car accelerates uniformly from rest to 15 m/s in 3.00s.

Question

(a) What is the work done on the car in this time interval?

 

(b) What is the power delivered by the engine in this time interval?

 

Answer 1

Hi Charlotte,

Part A

According to the work-energy theorem, the work done on an object is equal to the change in the (kinetic) energy of that object:

W = ΔKE = KE_f - KE_i = 1/2 (mv_f²) - 1/2 (mv_i²) = 1/2 (mv_f²) - 0

Notice the work done is NOT dependent on the time interval, so it wouldn't matter if it took us 3 seconds or 1 million seconds to increase the car's speed from zero to 15 m/s, the work done would be the same as long as the car has the same mass and change in velocity in both scenarios.

Part B

Power is equal to the work done divided by the time interval in which the work was done:

P = W / Δt = 1/2 (mv_f²) / 3 seconds

Notice that Power DOES depend on the time interval. The faster the work can be done, the more power is involved in the process. A more powerful engine for example can get you to the desired speed in a shorter time interval when compared to a less powerful engine.