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/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

Translation: KE₁ = 1/2 (2m) v₁² = 1/2[KE₂ = 1/2 (m) v₂²], and 1/2 (2m) (v₁ + 6)² = 1/2 (m) (v₂ + 6)². The first gives v₁² = 1/4 v₂² or v₂ = 2 v₁. Foiling the second expression: v₁² + 12v₁ + 36 = 1/2(v₂² + 12v₂ + 36) = 1/2(4v₁² + 24v₁ + 36) by substitution. Simplify: v₁² + 12v₁ + 36 = 2v₁² + 12v₁ + 16 and 20 = v₁² so v₁, v₂ = 4.47, 8.94 [m/s].