Jogger A has a mass m and a speed v, jogger B has a mass m/3 and a speed 3v, jogger C has a mass 4m and a speed v/3, and jogger D has a mass 3m and a speed v/2. Rank the joggers in order of increasing kinetic energy. Indicate ties where appropriate.

Kinetic energy for C < Kinetic energy for D < Kinetic energy for A < Kinetic energy for B

Explanation:

For jogger A

mass = m, speed = v

Kinetic energy of A = 0.5 x m v^2

For jogger B

mass = m/3, speed = 3v

Kinetic energy for B = 0.5 x m/3 x (3v) ^2 = 1.5 x mv^2

For jogger C

mass = 4m, speed = v/3

Kinetic energy for C = 0.5 x 4 m x (v/3) ^2 = 0.22 m v^2

For jogger D

mass = 3 m, speed = v/2

Kinetic energy for D = 0.5 x 3 m x (v/2) ^2 = 0.375 mv^2

So, order for increasing kinetic energy

Kinetic energy for C < Kinetic energy for D < Kinetic energy for A < Kinetic energy for B