Question

How much work W must be done on a particle with a mass of m to accelerate it from a speed of 0.891 c to a speed of 0.989 c ? Express your answer as a multiple of mc2 to three significant figures.

I keep getting 4.87 as the answer but it says it is wrong.

Answer 1

According to work energy theorem

The change in the kinetic energy of an object is equal to the net work done on the object.

Hence

Initial kinetic energy is given by

And the final kinetic energy is

Now,

by plugging all the values we get

which gives

Joules

This is the work done to increase the speed from 0.891c to 0.989c