The engine of a 2000kg car has a power rating of 75kW. How long would it take (seconds) to accelerate from rest to 100 km/hr at full power on level road. Neglect drag and friction.

Answer: 10.29 sec.

Explanation:

Neglecting drag and friction, and at road level, the energy developed during the time the car is accelerating, is equal to the change in kinetic energy.

If the car starts from rest, this means the following:

ΔK = 1/2 m*vf ²

As Power (by definition) is equal to Energy/Time = 75000 W = 75000 N. m/seg, in order to get time in seconds, we need to convert 100 km/h to m/sec first:

100 (Km/h) * (1000m / 1 Km) * (3600 sec/1 h) = 27,78 m/sec

Now, we calculate the change in energy:

ΔK = 1/2*2000 Kg. (27,78) ² m²/sec² = 771,728 J

If P = ΔK/Δt, Δt = ΔK/P = 771,728 J / 75,000 J/sec = 10.29 sec.