Question

The power, P (watts) , of a car engine is proportional to the square of its speed, s ( m / s ) . When s = 15 , P = 2100 . Work out the speed (to 1 DP) when the power is 2200 watts

Answer 1

Answer:

The speed of the car engine is 15.4m/s

Step-by-step explanation:

Given

Power = 2100; when Speed = 15

Required

Find Speed when Power = 2200

The question says power is proportional to square of speed;

Mathematically;

$Power\ \alpha \ Speed^2$

Represent Power with P and Speed with S

$P\ \alpha \ S^2$

Convert proportion to an equation

$P\ = \ kS^2$

Where k is proportionality constant

Make k the subject of formula

$\frac{P}{S^2} = k$

When P = 2100 and S = 15

$\frac{2100}{15^2} = k$

When P = 2200 and S is unknown

$\frac{2200}{S^2} = k$

Recall that $\frac{2100}{15^2} = k$

So;

$\frac{2200}{S^2} = k$ becomes

$\frac{2200}{S^2} = \frac{2100}{15^2}$

Cross Multiply

$S^2 * 2100 = 2200 * 15^2$

$S^2 * 2100 = 2200 * 225$

$S^2 * 2100 = 495000$

Divide both sides by 2100

$S^2 = \frac{495000}{2100}$

$S^2 =235.714285714$

Take Square Roots of both sides

$S = \sqrt{235.714285714}$

$S =15.3529894716$

$S = 15.4$ (Approximated)