# A-level Physics (Advancing Physics)/Kinematics

Kinematics is the study of how objects move. One needs to understand a situation in which an object changes speed, accelerating or decelerating, and travelling a certain distance. There are four equations you need to be able to use which relate these quantities.

## Variables[edit]

Before we can understand the kinematic equations, we need to understand the variables involved. They are as follows:

- t is the length of the interval of time being considered, in seconds.
- v is the speed of the object at the end of the time interval, in ms
^{−1}. - u is the speed of the object at the beginning of the time interval, in ms
^{−1}. - a is the acceleration of the object during the time interval, in ms
^{−2}. Has to be a constant. - s is the displacement (distance traveled) of the object during the time interval, in meters.

## Equations[edit]

The four equations are as follows:

1.

2.

3.

4.

## Derivations[edit]

It is also useful to know where the above equations come from. We know that acceleration is equal to change in speed per. unit time, so:

(*)

(1)

We also know that the average speed over the time interval is equal to displacement per. unit time, so:

(2)

If we substitute the value of v from equation 1 into equation 2, we get:

(3)

If we take the equation for acceleration (*), we can rearrange it to get:

If we substitute this equation for t into equation 2, we obtain:

(4)

## Questions[edit]

1. A person accelerates from a speed of 1 ms^{−1} to 1.7 ms^{−1} in 25 seconds. How far has he travelled in this time?

2. A car accelerates at a rate of 18 kmh^{−2} to a speed of 60 kmh^{−1}, travelling 1 km in the process. How fast was the car travelling before it travelled this distance?

3. A goose in flight is travelling at 4 ms^{−1}. It accelerates at a rate of 1.5 ms^{−2} for 7 seconds. What is its new speed?

4. How far does an aeroplane travel if it accelerates from 400 kmh^{−1} at a rate of 40 kmh^{−2} for 1 hour?