Posted by Taylor on .
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?

UnivPhys 
drwls,
M1 is the heavier car and the mass of the other car is M2 = M1/2
Orginally,
(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
Also,
(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