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:
[tex]E = \frac{1}{2} mv^{2} = Fx[/tex]
m: mass of the truck
v: velocity of the truck
The ratio between the first and the second example would be:
[tex]\frac{\frac{1}{2}mv_1^{2}}{\frac{1}{2}mv_2^{2}} = \frac{Fx_1}{Fx_2}[/tex]
This expression simplifies to:
[tex]\frac{v_1^{2} }{v_2^{2} } =\frac{x_1}{x_2}[/tex]
Inserting the speeds will give the ratio for x₁/x₂:
[tex]\frac{x_1}{x_2} = \frac{40^{2} }{80^{2} } = \frac{1}{4}[/tex]
The distance x₂ is 4 times longer then the distance x₁.
