# Equations of Motion

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## Equations of Motion

If acceleration is constant, a quicker way than drawing graphs to find acceleration, velocity or displacement is to use some equations.

The symbols for displacement, initial velocity, etc. are shown on the diagram.

Distance travelled s = average speed x t

So,

So,

So,

at = v - u

and v = u + at

Here's where is gets a bit more tricky. We can use the two equations in the boxes above to find two more equations:

v = u + at

So we can get rid of t by putting it in ↑

And finally...

It's quite rare to be asked to prove the last two equations, so don't panic too much!

The important thing is that you can use and remember the main equations.

Provided the acceleration is constant, you can now use the equations to calculate the velocities, displacements and accelerations.

Remember:

s = displacement

u = initial speed

v = final speed

t = time

a = constant acceleration.

Question:

A car starts travelling at 3 m/s and accelerates for 10 s at 5 m/s2.

Why mass is so unimportant!

If you have already looked at energy you will be familiar with:

Potential Energy = mgh and Kinetic Energy = ½ mv2

The potential energy lost as something falls is changed into kinetic energy it gains, so:

PE lost = KE gained

or, mgh = ½ mv2

So, gh = ½ v2 and therefore,

So velocity is independent of mass when an object is falling under gravity. This is assuming there is no air resistance, so no energy is converted to heat through friction.