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 6.0 m/s , they then have the same kinetic energy.

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 6.0 m/sm/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

2mv₁²/2 = 1/2mv₂²/2; v²₁ = v₂²/4; v₂ = 2v₁

2m(v₁ + 6)²/2= m(v₂ + 6)²/2; 2(v₁ + 6)² = (v₂ + 6)²; 2(v₁ + 6)² = (2v₁ + 6)²; 2v₁² + 24v₁ + 72 = 4v₁² + 24v₁ +

36; v₁² = 18; v₁ = 3√2 m/s = 4.24 m/s; v₂ = 6√2m/s = 8.49 m/s