Motion

Speed

The speed equation is one that you need to be able to recall and apply:Motion, figure 1

  • 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.Motion, figure 1

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/s2 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:Motion, figure 1Example: A car travels from rest (0m/s) to 60 m/s in 60 seconds, what is its acceleration?

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

Acceleration = 1m/s2

Average Acceleration

The second equation for acceleration is given to you in the exam:Motion, figure 1Example: In travelling 70cm along a rifle barrel, a bullet uniformly accelerates from rest to a velocity of 210m/s. Find the acceleration.

  1. Rearrange the equation for acceleration: a = (v2-u2)/2s
  2. Substitute in values: a = 2102-022 x 0.7
  3. Solve and include units

____Acceleration = 31,500m/s2

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:Motion, figure 1

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.

Try these:Motion, figure 2

Answers:

  1. 20m/s
  2. 0m/s2
  3. 4m/s2
  4. 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