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# 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/s^{2}.

**Why mass is so unimportant!**

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

Potential Energy = mgh and Kinetic Energy = ½ mv^{2}

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

**PE lost = KE gained**

or, mgh = ½ mv^{2}

So, gh = ½ v^{2} 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.