Question

The brakes in a car increase in temperature by ΔT when bringing the car to rest from a speed v. How much greater would ΔT be if the car initially had twice the speed? You may assume the car stops fast enough that no heat transfers out of the brakes.

a) ΔT would be twice as much.
b) ΔT would be four times as much.
c) ΔT would be half as much.
d) ΔT would be the same regardless of speed.

Answer 1

If the initial speed of a car is doubled, the kinetic energy would be four times greater, and since this energy is converted into heat, the temperature increase (ΔT) of the brakes would be four times as much. Therefore the correct answer is b) ΔT would be four times as much.

Step-by-step explanation:

The question is concerned with how the temperature increase (ΔT) in a car's brakes would change if the initial speed of the car is doubled. When a car is brought to rest, the kinetic energy due to its motion is converted into thermal energy, increasing the brakes' temperature.

The kinetic energy of the car is given by the equation E = 1/2 mv2, where m is the mass of the car and v is its initial velocity. If the initial velocity is doubled (2v), the kinetic energy becomes 1/2 m(2v)2 = 4(1/2 mv2), which is four times the original kinetic energy.

Therefore, if all this energy goes into heating the brakes and no heat is lost, the temperature increase would be four times as much, because ΔT is directly proportional to the amount of kinetic energy converted into heat.

The appropriate answer to the question is: b) ΔT would be four times as much.