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Representing and Measuring Motion |
Average Speed | Distance-Time Graph | Velocity-Time Graph | Acceleration and Deceleration
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Average Speed
In any journey, the speed of the vehicle will keep changing, but its average speed can be calculated if the total distance and time taken are known.
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average speed (m/s) |
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distance travelled (m)
time taken (s) |
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So if a cyclist travels 600 metres in 1 minute (60 seconds), his average speed will be:
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average speed |
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600
60 |
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10 m/s |
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Distance-Time Graph
If an object moves in a straight line, its distance from a certain point can be represented as a distance-time graph. |
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The line A-B shows a car travelling at a steady speed. It covers 2 km every 5 minutes.
Line C-D also shows a steady speed, but it is travelling slower and covers only 1 km every 5 minutes.
The gradient of the slope gives the speed of the object.
gradient
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distance covered
time taken |
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gradient of line A-B |
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6 km
15 minutes |
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0,4 km/min |
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gradient of line C-D |
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2 km
10 minutes |
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0,2 km/min |
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The steeper the slope of the graph, the greater the speed it represents.
The horizontal line, B-C, shows that the car has stopped.
The distance stays at 6 km from where the car set off. |
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Velocity-Time Graph
Velocity is speed in a given direction.
Velocity-time graphs can represent the movement of an object. |
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Between K and L, the velocity of the car is 0 m/s. It is stopped.
Between L and M, the car's velocity is increasing at a constant rate. Every second its velocity increases by 2,5 m/s.
A diagonal line shows an object is moving with constant acceleration.
The gradient of the line gives the acceleration.
| gradient of L-M |
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change in velocity
time taken |
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12,5 |
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5 |
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2,5 m/s2 |
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The steeper the slope of the line, the greater the acceleration.
Between M and N, the velocity stays at 12,5 m/s.
A horizontal line shows a constant velocity.
The area under a velocity-time graph represents the distance travelled.
| area under line L-M |
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½ x height of triangle x base of triangle |
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½ x 12,5 x 5 |
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31,25 |
So the car covered 31,25 m whilst accelerating.
| area under line M-N |
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height of rectangle x width of rectangle |
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12,5 x 2,2 |
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27,5 |
| So the car travelled 27,5 m at a constant velocity. |
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| total distance travelled |
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31,25 + 27,5 |
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58,75 m |
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Acceleration and Deceleration
Acceleration is the rate at which the velocity of an object changes.
This equation is used to calculate the steady acceleration of an object, travelling in a straight line.
acceleration (m/s2) |
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change in velocity (m/s) |
| time taken for change (s) |
If a car accelerates from a velocity of 10 m/s to 50 m/s in 5 seconds, its acceleration will be:
acceleration |
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(50 – 10) |
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5 |
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40 |
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5 |
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8 m/s2 |
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The rate that an object's velocity decreases is called its deceleration.
It is calculated using the same equation.
If a car is travelling at 20 m/s and it comes to a halt in 5 s, its deceleration is:
deceleration |
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(20 – 0)
5 |
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20
5 |
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4 m/s2 |
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