# Motion

## Speed

The speed equation is one that you need to be able to recall and apply:

- v = speed (m/s)
- s = distance (m)
- t = time (s)

Before you ask ‘why is speed ‘v’ and distance ‘s’?

The reason is because ‘v’ and ‘s’ really stand for **velocity** and **displacement** but we are using them for speed and distance as well.

In order to guarantee that we do not make any errors, we should **write out the equation in words**, rather than symbols in an exam.

Always remember to **convert units**!! If the answer wants time in seconds, but in the question it is in minutes, remember to multiply by 60.

This equation can be rearranged:

Distance = Speed x Time

Time = Distance / Speed

## Distance Time Graphs

A distance time graph can be created for **objects that move in a straight line**. The speed can be calculated from the **gradient** of the graph.

We can see it has four sections.

The first is when the object is moving away at a **constant speed**. We can calculate this speed from the gradient:

15 / 5 = 3m/s

The second shows the object moving at a slower speed:

5 / 10 = 0.5m/s

The third section is the **stationary** section. At this point the object is not moving. It is important to remember that **whenever you have a flat line, the object is not moving**.

The fourth section shows the object returning to its **original starting position** since it is is moving backwards down the number line.

## Acceleration

What is acceleration?

Acceleration is the **amount the velocity of an object changes in 1s**.

E.g. An acceleration of 2m/s^{2} means the velocity increases by 2m/s every second.

There are two acceleration equations that you are required to use. The first of which is one that you need to be able to recall and apply:Example: A car travels from rest (0m/s) to 60 m/s in 60 seconds, what is its acceleration?

- Work out the
**change in velocity**by taking the starting velocity away from the final velocity. 60m/s - 0m/s = 60m/s - Divide the change in velocity by the__ time__. 60÷60 = 1
- Make sure that you have included
**units**.

Acceleration = 1m/s^{2}

## Average Acceleration

The second equation for acceleration is given to you in the exam:Example: In travelling 70cm along a rifle barrel, a bullet uniformly accelerates from rest to a velocity of 210m/s. Find the acceleration.

- Rearrange the
**equation for acceleration**: a = (v^{2}-u^{2})/2s **Substitute**in values: a = 2102-022 x 0.7**Solve**and include**units**

____Acceleration = 31,500m/s^{2}

## Velocity Time Graphs

We have already discussed **distance time** graphs, __velocity time __graphs are similar but with a few extra details. Let’s have a look at an example:

```
1) The horizontal line at this point has a velocity of 0m/s. This means that the object is __stationary__ or at rest.
2) Steep line upwards shows an increase in velocity. This means that there is a __constant acceleration__.
3) At point 3 we are travelling at a __constant velocity__.
4) Steep line downwards comes with a __decreasing velocity__. This means that the object is decelerating or has a negative acceleration. This is also a constant value. It can also be seen the the deceleration is less than the acceleration in section 2. This is because the line is less steep.
```

Answers:

- 20m/s
- 0m/s
^{2} - 4m/s
^{2} - 2200m

- A train travels 80 miles in 1 hour 15 minutes. Calculate its average speed in mph.
- 64mph

Explanation:*Don't forget to include units* - A lizard accelerates from 3 m/s to 30 m/s in 9 seconds. What is the lizard’s average acceleration?
- 3m/s^2