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 , they then have the same kinetic energy.

What were the original speeds of the two cars?

Express your answers using two significant figures separated by a comma.

Answer 1

mass of the smaller car = m
mass of the larger car = 2m
initial velocity of the smaller car = v
initial velocity of the larger car = V

twice the larger car's initial kinetic energy equals the smaller car’s

2*{ ½*(2m)V²) = ½*m*v²
2*m*V² = ½*m*v²
V = v/2

Now increasing each velocity by 12 m/s

{½*(2m)*(V+12)²} = ½*m*(v+12)²
(V+12)² = ½*(v+12)²
replacing V with v from above solution
(v/2+12)² = ½*(v+12)²

(v²/4+12v+144) = ½*(v²+24v+144)

v²+48v+576 = 2v²+48v+288

v² = 288

v = 16.97 m/s

V = 8.48 m/s

original speeds of the two cars (17,8.5)