If Velocity Is Relative, Why Isn’t Kinetic Energy Relative?

Maybe that title isn’t super clear. How about I just present a question that seems popular online right now. It goes like this.

Velocity is relative so that increasing from 10–20 meters per second should be the same as increasing from 0–10 m/s in a moving reference frame. However, the change in kinetic energy from 10–20 m/s is 3 times the change in KE from 0–10 m/s. What’s up with that?

OK, let’s just check real quick.

Calculating the Change in Kinetic Energy

Just a quick reminder — we can calculate the kinetic energy of an object as:

Just to make the numbers easy, let’s say that we have an object with a mass of 2 kilograms (so that 1/2 m = 1). Let’s calculate the change in kinetic energy for these two cases:

Yup, that’s three times as much even though both cases have the same change in velocity (increase in 10 m/s).

Single Object, Constant Force

We can figure out what’s going on by imagining that both objects are accelerated by some external and constant…