Question

Two identical cars are on a test track. Car A goes from rest to 25 m/s in 8 seconds. Car B goes from rest to 25 m/s in 6 seconds. Which car required more power to get to 25 m/s? How can you tell?

Answer 1

Explanation:

Let the mass of each car is m.

Car A : initial velocity, u = 0, final velocity, v = 25 m/s, time, t = 8 second

Use first equation of motion to find the acceleration of the car A.

v = u + at

25 = 0 + a x 8

a = 3.125 m/s²

Car B : initial velocity, u = 0, final velocity, v = 25 m/s, time, t = 6 second

Use first equation of motion to find the acceleration of the car A.

v = u + at

25 = 0 + a' x 6

a' = 4.17 m/s²

As the acceleration of car B is more than the car A, so the car B applies more force, so it needs more power.

Thus, car B require more power than A.

Answer 2

The power required for car B is more compared to car A.

Explanation:

Let mass of car be m.

Kinetic energy = 0.5mv²

Change in Kinetic energy for car A = 0.5 x m x 25²-0.5 x m x 0²=312.5 m

Change in Kinetic energy for car B = 0.5 x m x 25²-0.5 x m x 0²=312.5 m

Power is the ratio of energy to time.

`\texttt{Power of car A = }(312.5m)/(8)=39.06m\\\\\texttt{Power of car B = }(312.5m)/(6)=52.08m`

The power required for car B is more compared to car A.