# Physics A Level revision: Kinematic equations

The fun bit of physics: AS and A level revision of kinematic equations for use in mechanics and projectiles. Looking at displacement, velocities, acceleration and time taken for bodies to move.

Kinematics describe how objects move. Acceleration, time, velocity and displacement are all considered in a situation. There are a number of kinematic equations which you need to know about and be able to use to solve problems.

### Variables

There are 5 variables which are used in kinematic equations:

• u – the initial velocity of the object
• v – the final velocity of the object
• t – the length of time being considered
• s – the displacement of the object
• a – the acceleration of the object

### Equations

The four kinematic equations are:

$\fs6 v = u + at$

$\fs6 s = ut + \frac{1}{2}at^2$

$\fs6 s = \frac{u + v}{2}t$

$\fs6 v^2 = u^2 + 2as$

These equations can be rearranged and also merged to give rise of new equations, you are expected to be use basic algebra techniques to rearrange the kinematic equations. Remember the basic rule: what you do to one side must be done to the other and you’ll be fine.

### Solving problems

To solve problems involving kinematic equations you should firstly write down all the variables you have been given together with the variable you want to find. You then need decide which equation is best to find the missing variable.

Example question: A car accelerates at a steady rate from rest at a set of traffic lights. 100 metres down the road the car is going at 30ms-1, what is the acceleration of the car?

Worked solution: Make a note of what we know and what we want to find out:

• u – 0
• v – 30ms-1
• t – irrelevant for this question
• s – 100m
• a – ???

We want to find a and we have values for u, v and s. The best equation for this is $v^2 = u^2 + 2as$ however it will require to be rearranged to find a. Firstly subtract u2 from both sides:

$\fs3 v^2 - u^2 = 2as$

Then divide both sides by 2s:

$\fs4 \frac{v^2 - u^2}{2s} = a$

Now we just put in the values we have:

$\fs4 \frac{30^2 - 0^2}{2\text{ x }100} = a$

And evaluate the equation:

$\fs4 \frac{900}{200} = 4.5ms^{-2} = a$