Question

A bus driver makes an emergency stop by slamming on the bus's brakes. Later, he slams on the brakes

again with the same amount of force but this time his speed is twice as much as the first time. How far will
the bus skid compared to the first time?
A. The stopping distance stays the same.
B. The stopping distance is doubled.
C. The stopping distance is quadrupled.
D. The stopping distance is tripled.
E. The mass of the bus is required.​

Answer 1

C. The stopping distance is quadrupled

Answer 2

Answer: Option C

Explanation: Let's do a heavy simplification.

The kinetic energy of the bus is K = (m/2)*v^2

Where m is the mass of the bus, and v is the velocity of the bus.

When the brakes are used, we can do a linear relationship that gives us the distance that the bus needs to come to a full stop, and this will depend on the kinetical energy that the buss had just right before, so the distance that the bus moves after slamming on the brakes is:

D = K/F = ((m/2)*v^2)/F

Where F depends on the effectiveness of the brakes, as bigger F is, faster the bus comes to a full stop.

Now, if we double the velocity; we have:

D' = ((m/2)*(2*v)^2)/F = ((m/2)*4*v^2)/F = 4*(((m/2)*v^2)/F) = 4*D

D' = 4D

So the distance is quadrupled, then the correct option is C