1. Speed and Acceleration
KS4 Physics
Speed and Acceleration

2. Speed and Acceleration
Contents
Speed and Acceleration
Stopping distance
Plotting the speed / time graph
Formula triangles
Summary activities

3. Stopping distance = thinking distance + braking distance
Stopping distances
How long does it take a moving vehicle to stop?  
Braking distance is the distance travelled whilst the brakes are being applied.
Thinking distance is the distance travelled before the brakes are applied.
Stopping distance is the sum of the thinking distance and the braking distance.
Stopping distance = thinking distance + braking distance

4. Definitions Stopping distance Friction Thinking distance
Braking distance
One of forces the road exerts on the tyres as the car is stopping.
The distance a car travels whilst it is braking.
The distance a car travels before the brakes are applied.
The sum of thinking distance and the braking distance.

5. What affects braking/thinking distance?
Braking distance
Speed of car
Speed of car
Drugs and alcohol
Road conditions
Tiredness
Condition of tyres
Medication
Condition of brakes
Medication
Condition of tyres
Tiredness
Condition of brakes
Drugs and alcohol
Road conditions
Speed of car

6. Medication, drugs/alcohol, speed of car, tiredness
Braking car questions
A car is moving along an open road. Suddenly, a sheep walks into the road.
What do we call the distance the car travels before the driver applies the brakes?
Name one factor that could increase the distance the car travels in this time.
The braking distance for the car is 35m. If the stopping distance is 50m, how far did the car travel before the driver applied the brakes?
Thinking distance
Medication, drugs/alcohol, speed of car, tiredness
Thinking distance = Stopping distance – braking distance
= 50m – 35m
= 15m

7. Car graphing activity – instructions
This graphing experiment shows an animation of a car travelling along a straight road.
1. Copy the results table shown on the next slide and complete it as the movie is played.
2. Record the distance the car has travelled every five seconds.
3. Plot a graph of your results.
Suggested teacher’s approach:
DISTANCE TIME GRAPH
Instruct students to copy the blank results table for the distance / time graph. (Note that the “answers” are animated on here – so avoid showing unless wanted).
Play the car animation so that students can record the results.
Instruct students on graphing their results.
Two Distance-Time graphs are included here. The first is plotted with 5 second intervals; the other with every data point included.
There are then two further animated graphs with a number of animations to help illustrate various points.
(Teachers might like to use a formula triangle for the Speed = distance/time equation – but this has not been included in the animated sequence.)
SPEED / TIME GRAPH
8. Repeat the procedure for the Speed / Time graph.
9. Make the point to students that they should draw smooth curves through their points – unlike the results using Excel. 10. Relate the Speed / Time graph back to the Distance / Time graph – in particular as regards the value for speed in the middle section of the graph.
THE CAR ANIMATION
10. On slower processors the animation will play more slowly than its design speed. Although this may detract from the “appeal” of the animation, the experiment will still work as the “seconds” displayed work independently of the play-back speed.
EMBEDDED EXCEL
11. The graphs are plotted using embedded Excel worksheets. These allow the data to be accessed by double clicking while in edit mode.
12. As Excel doesn’t use smooth curves for graphs this gives rise to slightly different shapes for the Speed / Time graphs when comparing plotting every five seconds, compared to every second. This would make a discussion point for G&T students on the need to draw smooth curves.

8. Car graphing activity – results table layout
Results table for distance/time graph
Time/seconds
Distance/metres 5 10 15 20 25 30 35 40 45 50 55

9. Car graphing activity – animation

10. Car graphing activity – results
Results table for
distance/time graph
Time/seconds
Distance/metres 5 16 10 76 15
186 20
234 25
484 30
634 35
784 40
904 45
974 50
994 55

11. Car graphing activity – results graph

12. Car graphing activity – results graph analysis
The speed of the car is changing – the graph is not flat. The slope of the graph is less steep as the car begins
to slow down.
The car has stopped. The graph is flat – the distance of the car from the start point is not changing.
The graph is straight – there is no change in speed.
The car is going fast but at a constant speed.
The graph is straight in this part of the journey.
The car is starting to move. The curve shows that
the speed is changing. The curve is upwards as the
car accelerates at the start of the journey.

13. Gradient of a distance/time graph
The speed of the car can be calculated by looking at the gradient of the distance/time graph.
Speed is “Distance Travelled divided by Time Taken”
These values can be read off the distance/time graph at different points, and this is the same as the gradient of the graph.

14. Gradient of a distance/time graph
Consider the gradient of this graph at the point shown by the two arrows in a triangle:
The car has travelled from 200m to 800m = 600m.
It took from 16s to 36s to travel this distance = 20s.
So the speed at this point = 600m/20s = 30m/s.

15. Speed and Acceleration
Contents
Speed and Acceleration
Stopping distance
Plotting the speed / time graph
Formula triangles
Summary activities

16. Plotting the speed / time graph
Having looked at the distance-time graph, plot the speed-time graph:
Copy the results table shown on the next slide and complete it as the movie is played
Record the speed of the car at five second intervals.
Then graph your results.

17. Car graphing activity – results table layout
Results table for
speed/time graph
Time/seconds
Speed (m/sec) 5 10 15 20 25 30 35 40 45 50 55

18. Car activity – animation

19. Car graphing activity – results
Results table for
speed/time graph
Time/seconds
Speed (m/sec) 5 6 10 16 15 26 20 30 25 35 40 45 50 55

20. Speed / time graph for a car
Car at rest – zero speed
Car at constant speed – acceleration is zero.
Car decelerating – speed is decreasing.
Care accelerating – speed is increasing.

21. Speed / time graph for a car
From both graphs we can see that the speed is 30 m/s.
(Using the value calculated previously)
Now compare the Speed / Time graph with the earlier Distance / Time graph
The speed is increasing, and we can see that the Distance / Time graph curves upwards.
The speed is decreasing and the curve is downwards
The speed is zero – the car is not moving
– and we can see that the distance that the car has travelled is not changing either.

22. Speed and Acceleration
Contents
Speed and Acceleration
Stopping distance
Plotting the speed / time graph
Formula triangles
Summary activities

23. speed = distance ÷ time s = d/t
Calculating speed
We can express the speed formula using the equation:
speed = distance ÷ time
s = d/t
Speed measured in metres per second (m/s)
Distance measured in metres (m)
Time measured in seconds (s)

24. Speed formula triangle
Formula triangles help you to rearrange formula. The triangle for the speed formula is shown below.
Cover up whatever quantity you are trying to find, and you will be left with the calculation required.
3) …and you are left with the sum…
s = d ÷ t
1) So if you were trying to find speed (s)… d  
2) …you would cover up s… s t x

25. Interactive formula triangle

26. Speed of vehicles
Measure out a known distance, say 100m, alongside a road.
Record the time it takes vehicles to cover the distance.  
100 m
Use the speed formula, s=d/t, to calculate the speeds of various vehicles.
Measure the speed of at least 20 vehicles and then represent your data graphically.

27. Calculating acceleration
We can express the formula for acceleration using the equation:
acceleration = change in velocity ÷ time taken
a = c/t
Acceleration is measured in metres per second per second (m/s2)
Change in velocity is measured in metres per second (m/s)
Time measured is in seconds (s)

28. Acceleration formula triangle
Formula triangles help you to rearrange formula. The triangle for the acceleration formula is shown below.
Cover up whatever quantity you are trying to find, and you will be left with the calculation required.
1) So if you were trying to find acceleration (a)...
3) …and you are left with the sum…
a = c ÷ t c  
2) …you would cover up a… a t x

29. Speed and Acceleration
Contents
Speed and Acceleration
Stopping distance
Plotting the speed / time graph
Formula triangles
Summary activities

30. Glossary
acceleration – The rate of change of velocity per unit time. It is measured in metres per second squared (m/s2).
braking distance – The distance a car travels while the brakes are being applied.
friction – The force that tries to stop materials moving over each other. It occurs between a road surface and car tyres.
speed – How fast an object is moving. It equals the distance moved divided by the time taken and is usually measured in metres per second (m/s).
stopping distance – The total distance needed to stop a car. It is the thinking distance plus the braking distance.
thinking distance – The distance a car travels while the driver is thinking before the brakes are applied.
velocity – The speed at which an object is travelling in a particular direction. It is measured in metres per second (m/s).

31. Anagrams

32. Multiple-choice quiz