Question

The power, P (watts), of a car engine is proportional to the square of its speed, s (m/s).

When s = 35, P = 1760.
Work out the power (to 1 DP) when the speed is 40 m/s

Answer 1

P = 2288 W

Explanation:

The power, P (watts), of a car engine is proportional to the square of its speed i.e.

`P\propto s^2`

or

`P=ks^2`

Put s = 35, P = 1760 to find k.

`k=(P)/(s^2)\\\\k=(1760)/(35^2)\\\\k=1.43`

Now put k = 1.43 and s = 40. So,

`P=1.43* (40)^2\\\\P=2288\ W`

So, the new power is 2288 W when the speed is 40 m/s.