Also on this page: Distance-time graphs        Relative Motion      

The speed of an object tells you how fast it is moving.

You can calculate the average speed of an object if you measure:

  • The distance it has moved
  • The time it took to travel that distance

 

Average speed = distance ÷ time

Unit of speed  = metre/second (m/s)

 

 

Example 1

A model car takes 8s to travel 10m.
What is the Average speed of the car?
Speed = distance ÷ time
∴ speed = 10÷ 8
∴ speed = 1.25m/s

Example 2
A boy can cycle at an average speed of 10 kilometers per hour
How long will it take him to cycle 30km?


Use the formula Time =  distance ÷ speed

∴ Time = 30 ÷ 10
∴ Time = 3 hours

Distance – Time graphs
A distance-time graph is a useful way to represent the movement of an object.

Points to know:

  • The time taken is always on the horizontal (x) axis
  • The distance travelled is always on the vertical (y) axis
  • The steeper the line, the faster the travel
  • A horizontal line means the object is stationary
  • The speed can be worked out by dividing the distance reading of the graph by the time.

 

Example 1

Graph showing speed of a toy car

Section A:  the car took 20s to travel 2m
Section B: the car was stationary for 10s
Section C: the car took 5s to travel 2m

The total time for the experiment was 45s
The total time moving was 20s + 10s = 30s

The car travelled fastest during section C of the graph
(we know this because the line is steepest)

In section A the car travelled at an average speed of 20÷2 = 10 m/s

 

Questions
A girl timed a woodlouse walking around a tray on the laboratory bench and drew a distance-time graph of her results.

  1. For how many seconds was the woodlice moving? Answer

 

2. How many times did the woodlouse stop? Answer

3. What was the total time the woodlouse stopped for? Answer

4. How far did the woodlouse move?Answer

Relative motion

Sometimes you might be in a train over-taken by another train on a faster line.
The other train appears to moving quite slowly past your window even though you know it to be moving quite fast.
This is because of their relative motion to each other

How to calculate the relative speed:

  • If the trains are moving in the same direction
    the relative speed = faster speed – slower speed
  • If the trains are moving in opposite directions
    the relative speed = speed of train 1 + speed of speed 2

 

Questions
You are in a blue car on a motorway travelling at 25 m/s.
There is a red car behind you on the outer lane which is travelling at 32 m/s.
What is their relative speed (ie at what speed will the red car appear to overtake you)?
Answer

You are in a train travelling at 45m/s.
On the next line  there is another train travelling in the same direction at 50ms
What is the the relative speed of the two trains?
Answer

Two children are driving radio controlled cars which they drive into each other to make them crash.
Peter’s car is travelling at 3m/s and Alice’s car is moving at 5m/s.
What is their relative speed when they hit?
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