A car has 1000 kg mass and accelerates from 0 to 25m/s in 10 s. What will be the power of the car?
Power is the work done per unit time. The mass of the car is 1000 kg and work is done to increase its speed from 0 m/s to 25 m/s in 10 s.
The kinetic energy of an object with mass m and moving at v m/s is given by the expression (1/2)*m*v^2.
At rest, the kinetic energy of the car is (1/2)*1000*0^2 = 0 J. 10 seconds later it is moving at 25 m/s. The kinetic energy of the car is (1/2)*1000*25^2 = 312500 J.
In 10 s, the change in energy is 312500 J. The power required to achieve this is equal to 31250 W or 31.25 kW.