A 25.0 kg bumper car moving to the right at 5.00 m/s overtakes and col-
lides clastically with a 35.0 kg bumper car moving to the right. After the
collision, the 25.0 kg bumper car slows to 1.50 m/s to the right, and the
35.0 kg car moves at 4.50 m/s to the right.
a. Find the velocity of the 35 kg bumper car before the collision.
.b. Verify your answer by calculating the total kinetic energy before and
after the collision.

Explanation:

This problem bothers elastic collision.

Given data

Mass m1= 25kg

Initial velocity u1= 5m/s

Final velocity v1= 1.5m/s

Mass m2= 35kg

Initial velocity u2=?

Final velocity v2 = 4.5m/s

A. To find the initial velocity of the 35kg car, let us Apply the principle of conservation of energy

m1u1+m2u2= m1v1+m2v2

25*5+ 35*u2= 25*1.5+ 35*4.5

125+35u2= 37.5+157.5

125+35u2=195

35u2= 195-125

35u2= 70

u2= 2m/s

The initial velocity is 2m/s

B. Totally not kinetic energy before impact

KE= 1/2m1u1²+ 1/2m2u2²

KE= (25*5²)/2+ (35*2²)/2

KE= 625/2 +140/2

KE= 312.5+70

KE= 382.5J

Total kinetic energy after impact

KE=1/2m1v1²+ 1/2m2v2²

KE= (25*1.5²)/2 +(35*4.5²)/2

KE= 56.25/2 +708.75/2

KE=28.125 +354.375

KE= 382.5J

We can see that energy is conserved

Kinetic energy before and after impact remains unchanged

conservation of mass

mass before something happens = mass afterwards