Question

The first car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 12 m/s m/s , they then have the same kinetic energy. Part A What were the original speeds of the two cars?

Answer 1

Given Data:

• Mass of the car 1, (m1)=2m

• Mass of the car 2, (m2)=m

• Initial kinetic energy of the car 1, =K1

• Initial kinetic energy of the car 2, (K2)=2K1

Let us consider the initial velocity of the car 1 is "v" and that of car 2 is "V"

therefore

K2=2K1

½(m)V²=2×½(2m)v²

V²=4v²

V=2v

On increasing the velocity by 12 m/s, their kinetic energy becomes equal, therefore

K2=K1

½(m)(V+12)²=½(2m)(v+12)²

(V+12)²/(v+12)²=2

(2v+12)/(v+12)=√2

v=8.485 m/s

The initial speed of the car 2 would be

V=2v

V=2×8.485

V=16.97 m/s