# Prove Kinetic Energy equation (without calculus)

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1. Mar 19, 2015

### Chrystalle

1. The problem statement, all variables and given/known data
Prove kinetic energy is relationship between mass and velocity using E(g)=mgh (no calculus, momentum, kinematics).

2. Relevant equations
gravitational energy: E=mgh
kinetic energy: E=(1/2)mv^2

3. The attempt at a solution
I know it can be derived using the gravitational energy equation (E=mgh) and the kinematic equation (Δv^2)=2aΔx.

If I'm correct, conservation of energy (in free fall situation) states that E gravitational before being dropped = E kinetic when object hits the ground. I've been led to believe that I can prove the kinetic energy formula only needing E(g)=mgh and E(g)=E(k). This does not seem like enough information though. I'm stuck trying to prove that height doesn't affect kinetic energy and that the relationship between mass and velocity is (1/2) and ^2.

Am I wrong that kinetic energy can be derived only knowing E(g)=mgh and E(g)=E(k)?

2. Mar 19, 2015

### Shinaolord

E , when considering the total energy, isn't a function of k, it's a function of height (The potential part, The sum is obviously a constant), which in turn can be considered a function of time. $E(h(t))$

EDIT: what you are given is the only necessary info.

3. Mar 19, 2015

### Chrystalle

I thought energy was a poor tool for time?

4. Mar 20, 2015

### epenguin

Last edited: Mar 20, 2015