Q4. A car can deliver at most 60 kW of useful driving power after transmission losses. On a level road the total resistance is 2000 N. What is the car’s top speed?
At top speed the driving force equals the resistance, and all the power goes into overcoming it: v = P/F, that is 60 000/2000, or 30 m s (108 km/h).
Q5. A body of mass 2 kg starts from rest and a constant net force of 4 N acts on it. Find (a) the power delivered at t = 3 s and (b) the average power over the first 3 s.
(a) The acceleration is 4/2, that is 2 m s, so at 3 s the speed is 6 m s and P = Fv = 4 × 6, that is 24 W. (b) The work done in 3 s is the kinetic energy gained, , that is 36 J, so the average power is 36/3, that is 12 W, half the final power.
Q6. A geyser draws a constant 2 kW for 45 minutes every day. How much energy does it use in 30 days, in kWh?
Each day it uses 2 kW × 0.75 h, that is 1.5 kWh, so in 30 days it uses 1.5 × 30, that is 45 kWh.