Question

Q2. When the driver applies the brakes of a light truck traveling 40 km/h, it skids 3 m before stopping. How far will the truck skid if it is traveling 80 km/h when the brakes are applied

Answer 1

Answer:

12m

Explanation:

If the brake force F is constant the brakes have to do work: W = Fx, where x is the skid distance.

The work is necessary to remove the kinetic energy from the truck. It follows:

$E = \frac{1}{2} mv^{2} = Fx$

m: mass of the truck

v: velocity of the truck

The ratio between the first and the second example would be:

$\frac{\frac{1}{2}mv_1^{2}}{\frac{1}{2}mv_2^{2}} = \frac{Fx_1}{Fx_2}$

This expression simplifies to:

$\frac{v_1^{2} }{v_2^{2} } =\frac{x_1}{x_2}$

Inserting the speeds will give the ratio for  x₁/x₂:

$\frac{x_1}{x_2} = \frac{40^{2} }{80^{2} } = \frac{1}{4}$

The distance x₂ is 4 times longer then the distance x₁.