posted by Taylor .
One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 5.0m/s, they then have the same kinetic energy.
What were the original speeds of the two cars?
M1 is the heavier car and the mass of the other car is M2 = M1/2
(1/2) M1 V1^2 = (1/2)*(1/2)(M1/2)V2^2
which implies that
V1^2 = (1/4)V2^2
V1 = V2/2
(1/2)M1*(V1+5)^2 = (1/2)(M1/2)(V2+5)^2
= (1/2)(M1/2)(2V1 + 5)^2
(V1+5)^2 = (1/2)(2V1+5)^2
V1^2 + 10 V1 + 25 = 2V1^2 + 10 V1 + 25/2
V1^2 = 25/2
V1 = 5/sqrt2
V2 = 5 sqrt2