A 950 kg car accelerates from 0 ms to 25 ms in 5.0 seconds How much power does that require?

Answer 1

The kinetic energy (in joules, J) of an object travelling at a speed well below the speed of light is given by:

E = 1/2 m v2

where m is the mass in kilograms (kg), and v is the speed in metres per second (m s-1).

When the car is at rest, its kinetic energy is zero. At a speed of 25 m s-1, its kinetic energy is:

E = 1/2 x 950 kg x (25 m s-1)2

= 475 x 625

= 296 875 J

So it gained 296 857 joules of energy over a period of 5 seconds. The power is the rate at which energy is gained (or used up, depending on the situation), in joules per second (J s-1), which may also be called watts (W). The average power gained here is given by:

P = E / t

where t is the time (in seconds, s) that it took to transfer the energy E. So:

P = 296 875 / 5

= 59 375 W

or 59.375 kilowatts (kW)

You can round this to 59 kW, giving the answer to 2 significant figures (since the numbers in the question are quoted to that degree of accuracy).