Two bodies of equal masses are moving with uniform velocities v and 2v.Find the ratio of their of heir kinetic energies?

Answer 1

Kinetic energy is equal to the mass of the object times the velocity squared (Ek=.5mv2). To obtain the ratio between the two objects, divide the first by the second (Ek1/Ek2). This is equivalent to .5m1v12/.5m2v22. Since the masses are equal, they cancel out and you are left with v12/v22. Next, as stated in the problem, the seceond velocity is twice as much as the first so plug that coefficient into the aforementioned equation. (1v12)/(2v22). Since the values of velocity (v) are equal in this problem, they can cancel out just as the masses did. Now, 12=1 and 22=4; so the ratio is 1/4.

Answer 2

The ratio of the kinetic energies of two bodies with equal mass

is the square of the ratio of their speeds.