How much work must be done on a kg bicycle to increase its speed from 2 ms to 3 ms?

Answer 1

Kinetic Energy = 1/2 m V2

At 2 m/s, the bicycle's KE is (1/2 x 10 x 4) = 20 joules.

At 3 m/s, its KE is (1/2 x 10 x 9) = 45 joules.

The difference in kinetic energy at the higher speed is (45 - 20) = 25 joules.

That's the energy (work) that has to come from somewhere in order to achieve

the higher speed.

Check:

The ratio of speeds is 3/2 = 1.5 . Since kinetic energy is proportional to the square of the speed,

we need the square of the ratio to check. It's (1.5)2 = 2.25 .

The ratio of the kinetic energies that we calculated at the two speeds is (45/20) = 2.25 .

That's good enough for us. Check ! and mate