 Here we'll derive one more expression for relativistic energy. So we have momentum p equals gamma mv and energy e squared equals m squared c to the 4 plus p squared c squared. Now if we take the energy equation and substitute in the equation for momentum, we derive e equals gamma mc squared. What's the significance of this equation? Well so we know that if v is much smaller than c, gamma is approximately equal to 1. But we can get a slightly more accurate version. Using something called a Taylor series, which you'll learn about if you go on to do more maths in university, you'll see that gamma is approximately equal to 1 plus a half v squared on c squared. So as v is much smaller than c, this is really close to 1, we've just made this estimate a little bit more accurate. And if we substitute that in, you get e is equal to mc squared plus a half mv squared. So again we have the rest energy as well as a term that we'd recognize as the kinetic energy. And so again we see that when velocity is much smaller than c, this reduces to an expression that we're familiar with in our everyday life. Well it's true that we haven't seen the rest energy term before. Since it doesn't depend on our velocity or anything else we normally have access to, it just comes out as a constant. And as it's only changes in energy that are important, only the kinetic term will affect our lives. And just to convince you that our approximation is legitimate, here we plot both of these energy values. So the blue line is the true energy, e equals gamma mc squared, and the yellow line is our approximation mc squared plus a half mv squared. And you see the two are reasonably close for values less than about c on 5.