# Derive the equation for kinetic energy

1. Feb 24, 2015

### Suraj M

question:
I came across a question which said: Derive the equation for kinetic energy of a body of mass m and velocity v.
What do they mean?
Attempt:
I actually just wrote that by work energy theorem diff. in KE = work done
so Fx = KE
$$max = m \frac {v²-u²}{2x} x = ½mv² - ½mu²$$
each of these terms represents a quantity called KE so this is the formula.
Is this right?? Because i seriously doubt it.

2. Feb 24, 2015

### PeroK

That assumes constant acceleration. What if acceleration isn't constant?

3. Feb 24, 2015

### Suraj M

Then i would do this:
$$Fdx = dKE$$
$$ma.dx = m. \frac{dv}{dt}dx = m v dv$$
$$mvdv = dKE$$
$$m~₀∫^x vdv = ΔKE$$
$$\frac{m(v^2 - u^2)}{2} = ΔKE$$