1. Chapter 9&10 Revision Distance-time graphs Velocity and Acceleration
Velocity-time graphs
Forces and acceleration
Falling objects
Forces and Braking
Momentum
Forces and Elasticity
HIGHER TIER ONLY

2. Calculating Speed We can calculate the speed of an object
from knowing the distance travelled and
the time taken:
Speed (m/s) = Distance Travelled (m)
Time Taken (s)
Speed is measured in m/s

3. Try these examples…

4. Distance-time graphs Distance (m) Time (s)
The steeper the gradient, the higher the speed.
Distance goes on the y axis and is measured in metres.
Distance (m)
The gradient or slope of the line tells us about the speed.
Time goes on the x-axis and is measured in seconds
Time (s)

5. Calculating Speed from a distance-time graph – finding the gradient
time (s)
distance (m) 2 1 3 4 5 6 7 8 9 10 20 30 40 50 60 70 A B
Gradient = Change in distance
Change in time
Gradient = Distance at B – Distance at A
Time at B – Time at A
Gradient = 70m – 10m = 60m
6 –
Gradient = 20m/s

6. Have a go!
Teacher notes
This multiple-choice quiz could be used as a plenary activity to assess students’ understanding of calculating the speed from the gradient of a distance–time graph.

7. There are 3 shapes you should know….
1) Constant Speed
2) Speeding Up
3) Slowing down
Speed decreasing because gradient of line getting getting less steep.
Speed constant because gradient of the line doesn’t change
Speed increasing because gradient of line getting steeper
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8. Velocity and Acceleration

9. What is Velocity?
Velocity is the speed of an object in a given direction.
An object moving steadily round in a
circle has a constant speed but its velocity changes.

10. What is acceleration?
The acceleration of an object is a measure of how quickly its velocity changes.
A train accelerates in a straight line from rest. As it does, its velocity increases.
Photo credit (top left): Mike Vam
Photo credit (bottom right): Pete Smith
The brakes on this motorcycle are causing it to slow down. This is negative acceleration or deceleration.

11. How is acceleration calculated?
The acceleration of an object can be calculated using this equation:
change in velocity
time taken
acceleration =
Change in velocity is measured in metres per second (m/s).
Time taken is measured in seconds (s).
Acceleration is measured in metres per second per second (m/s2).

12. Example The velocity of a car increased from
8m/s to 28m/s in 8s without changing
direction. Calculate:
Its change of velocity
Its acceleration

13. Worked Answer a) Change in velocity = final vel. – initial vel
= 28 – 8
= 20m/s
b) Acceleration = Change in vel.
Time taken
= 20/8
= 2.5 m/s2

14. Try these….
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15. Velocity-time Graphs

16. Velocity-time graphs Velocity (m/s) Time (s)
The steeper the gradient, the faster the acceleration.
Velocity goes on the y axis and is measured in m/s.
Velocity (m/s)
The gradient or slope of the line tells us about the acceleration.
Time goes on the x-axis and is measured in seconds
Time (s)

17. Calculating acceleration from velocity-time graphs – finding the gradient.
time (s)
speed (m/s) 2 1 3 4 5 6 7 8 10 15 20 25 30 35 A B
the object’s speed has increased by 20 m/s (25 - 5)
it took 4 s to change speed (6 - 2)
acceleration = speed/time
= 20/4
= 5 m/s2

18. Try these…. Teacher notes
This multiple-choice quiz could be used as a plenary activity to assess students’ understanding of calculating the acceleration from the gradient of a speed–time graph.

19. Calculating distance from a velocity-time graph – finding the area.
Teacher notes
This six-part animated sequence provides a step-by-step guide to how the distance travelled by an object can be calculated from the area underneath its speed–time graph.
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20. Forces and Acceleration

21. 1) When the forces on a stationary object are balanced the object….
Stays still b) Accelerates c) Moves at constant speed.
2) When the forces on an object moving at constant speed are balanced the object…
Stays still b) Accelerates c) Moves at constant speed.
3) For a car moving with constant speed, what is happening in each of these situations?
a) slowing down b) speeding up c) constant speed.

22. Unbalanced Forces – Newton’s 2nd Law
If the resultant force acting on an object is not zero, all the forces are said to be unbalanced.
This forms the basis of Newton’s second law of motion, which states:
If the forces on an object are unbalanced, two things about the object can change:
the speed of the object may change – it may either increase or decrease
the direction of motion may change.

23. How is movement calculated from force?
The resultant force acting on an object is related to the object’s mass and acceleration. These three factors are linked by the following equation:
force = mass x acceleration
Resultant force is measured in newtons (N).
Mass is measured in kilograms (kg).
Acceleration is measured in metres per second per second (m/s2).

24. Worked Example – Don’t forget 3 steps!
A car has a mass of 1,000 kg. What force must the car’s engine supply to cause an acceleration of 2 m/s2?
force = mass x acceleration
Photo credit: Piotr Gilko
= 1,000 x 2
= 2,000 N

25. F = ma calculations HOME Teacher notes
Question 2 aims to get students to think laterally and work out that acceleration due to gravity (10m/s2) is needed to complete the calculation.
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26. Falling Objects

27. Terminal velocity of a skydiver
Boardworks GCSE Additional Science: Physics
Laws of Motion
Terminal velocity of a skydiver
Teacher notes
The terminal velocity for a skydiver is around 60m/s, but varies with factors such as the weight and the shape of person.

28. Velocity–time graph of skydiver
Boardworks GCSE Additional Science: Physics
Laws of Motion
Velocity–time graph of skydiver
Teacher notes
This animated and interactive graph provides an opportunity for students to apply their knowledge of velocity–time / speed–time graphs to explain the descent of a skydiver. While it continues the theme of balanced forces, the graph could also introduce the idea of unbalanced forces leading to acceleration and deceleration.
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29. Forces and Braking

30. On the road - Why have speed limits?
Speed limits are an important part of road safety. They aim to prevent drivers from driving at speeds that are unsuitable and unsafe.
The faster a vehicle is driving, the longer it will take to stop – the overall distance this takes is the stopping distance.
Teacher notes
See the ‘Energy and Movement’ and ‘Momentum’ presentations for more information about the speed and safety of a vehicle in terms of kinetic energy, momentum and force.
stopping distance = thinking distance + braking distance

31. What affects thinking distance?
The thinking distance is the distance a vehicle travels in the time it takes for a driver to react to a situation and apply the brakes.
What factors will affect thinking distance?
alcohol
other drugs and some medicines
tiredness
speed
distractions, such as mobile phones

32. What affects braking distance?
The braking distance is the distance a vehicle takes to stop once the driver has applied the brakes.
What factors will affect braking distance?
weather
condition of tyres/brakes
speed
condition of road

33. Factors affecting stopping distances
Boardworks GCSE Additional Science: Physics
Speed and Acceleration
HOME
Factors affecting stopping distances
Teacher notes
Appropriately coloured voting cards could be used with this classification activity to increase class participation.

34. Momentum
HIGHER TIER ONLY

35. Stopping moving objects
Why is it a good idea to avoid a large object moving quickly?
HIGHER TIER ONLY

36. What is momentum?
All moving objects have momentum. This is a measure of how difficult it is to stop a moving object.
If these two cars have the same mass but one is quicker than the other, which has the most momentum?
The faster car.
If both cars travel at the same velocity, but one is full with luggage and the other is empty, which will have the most momentum?
The heavier car.
The bigger an object is and the faster it moves, the more momentum it will have and the more difficult it will be to stop.
HIGHER TIER ONLY

37. How is momentum calculated?
The momentum of an object can be calculated using this equation:
momentum = mass x velocity
Mass is measured in kilograms (kg).
Velocity is measured in metres per second (m/s).
Teacher notes
It may be worth pointing out to students that the force needed to lift an object is the same as the weight of the object. For example, the force needed to lift a 100N box is 100N.
Momentum is measured in kilogram metres per second (kg m/s).
It is a VECTOR quantity! Direction matters!
HIGHER TIER ONLY

38. Calculating momentum question
An aircraft carrier has a mass of 1,000,000 kg and a velocity of 15 m/s. What is its momentum?
momentum = mass x velocity
Photo credit: Robert Linder
= 1,000,000 x 15
= 15,000,000 kg m/s
HIGHER TIER ONLY

39. Momentum calculations
Boardworks GCSE Additional Science: Physics
Momentum
Momentum calculations
HIGHER TIER ONLY

40. Using conservation of momentum
Boardworks GCSE Additional Science: Physics
Momentum
Using conservation of momentum
Teacher notes
This five-stage animation shows how the principle of conservation of momentum can be used to calculate the velocity of an object.
HIGHER TIER ONLY

41. Conservation of momentum question
Two trolleys collide and stick together. From the data below, calculate the velocity of the trolleys after the collision.
trolley A
trolley B
mass = 3 kg
mass = 5 kg
velocity = 8 m/s
velocity = -4 m/s
momentum = 24 kg m/s (3 x 8)
momentum = -20 kg m/s (5 x -4)
total momentum before collision = 4 kg m/s ( )
momentum after collision = 4 kg m/s
mass after collision = 8 kg (3 + 5)
velocity after collision = momentum / mass = 0.5 m/s
HIGHER TIER ONLY

42. Momentum in explosions
Boardworks GCSE Additional Science: Physics
Momentum
Momentum in explosions
Teacher notes
This six-stage animation shows momentum during an explosion.
HIGHER TIER ONLY

43. Momentum: true or false?
Boardworks GCSE Additional Science: Physics
Momentum
Momentum: true or false?
Teacher notes
This true-or-false quiz could be used as a starter exercise to work on momentum. Students could be given coloured traffic light cards (red = false, green = true) to vote on the statements shown. To stretch students, they could be asked to explain their voting.
HIGHER TIER ONLY

44. Force and change in momentum
When a force is applied to an object, the object’s velocity changes. This means that its momentum will also change.
The change in momentum depends on the size of the force and the time for which it is applied. The relationship between this values is shown by this equation:
force = change in momentum
time
Momentum is measured in kilogram meters per second (kg m/s).
Time is measured in seconds (s).
Force is measured in newtons (N).
HIGHER TIER ONLY

45. Change in momentum question 1
A rugby ball of mass 0.5 kg is kicked from stationary to a velocity of 8 m/s. The kicker’s foot is in contact with ball for 0.1 seconds. What force does the kicker use?
force =
change in momentum
time
= (0.5 x 8) – ( 0.5 x 0)
0.1
Photo credit: Ben Hodgson
= 4
0.1
= 40 N
HIGHER TIER ONLY

46. Change in momentum question 2
A tennis ball is rolled at a toy car of mass 0.1 kg. The car is moved with a velocity of 0.5 m/s. If the ball and car are in contact for 0.05 seconds, with what force is the tennis ball is rolled?
force =
change in momentum
time
= (0.1 x 0.5) – ( 0.1 x 0)
0.1
Photo credit: Hervé de Brabandère
= 0.05
0.05
= 1 N
HIGHER TIER ONLY

47. Change in momentum calculations
Boardworks GCSE Additional Science: Physics
Momentum
Change in momentum calculations
HIGHER TIER ONLY

48. Car crashes and momentum
What happens if two cars travelling very quickly collide?
Both cars come to a stop in a short space of time. This means that the cars and their occupants experience a large change of momentum very quickly. Why could this cause a very serious injury?
Photo credit: Volvo Car Corporation, Public Affairs, SE Gothenburg
A very large change of momentum in a short space of time means the car occupants will experience a very large force.
Using this principle, how could you improve the safety of cars?
HIGHER TIER ONLY

49. Reducing force in car crashes
Many modern car safety features work by increasing the amount of time taken for the person to decelerate in a collision. How does this reduce the risk of serious injury?
A longer deceleration means that change in momentum occurs over a longer time. There is therefore a smaller
force acting on the person.
What features of cars use this principle?
Photo credit: Volvo Car Corporation, Public Affairs, SE Gothenburg
seatbelts
airbags
crumple zones
HIGHER TIER ONLY

50. How do car safety features work?
Boardworks GCSE Additional Science: Physics
Momentum
How do car safety features work?
Photo credit: Volvo Car Corporation, Public Affairs, SE Gothenburg
Teacher notes
This guide to car safety features could be used ahead of an ICT extension topic. Students could use the internet to research the effects that seatbelts, airbags and crumple zones have had in terms of saving lives and reducing serious injury. They could present their findings in the style of scientific paper or presentation to the class or in small groups.
More information about seatbelts is available at:
HOME
HIGHER TIER ONLY

51. Forces and Elasticity

52. Stretching and Squashing
A steel spring is loaded up with increasing masses so that the force applied increases (F) and the extension of the spring (x) is recorded.
THIS IS A CORE PRAC – COULD YOU DESCRIBE HOW TO CARRY IT OUT?

53. Key Points
Hooke’s Law = The amount a spring stretches is directly proportional to the amount of force applied to it.
RULES FOR DIRECTLY PROPORTIONAL:
Straight line
Passing through origin.
F = k ∆x

54. What does k mean in F=k∆x?
k is called the spring constant and is a measure of the stiffness of the spring or material
It can be found from the gradient of a F-x graph
It has units of Nm-1 (newtons per metre)
The higher the k the stiffer the spring

55. The spring constant k is measured in Nm-1 because it is the force per unit extension.
The value of k does not change unless you change the shape of the spring or the material that the spring is made of.

56. Example
A spring is 0.38m long.
When it is pulled by a force of 2.0 N, it stretches to 0.42 m.
What is the spring constant? (Assume the spring behaves elastically.)
Extension, x = Stretched length – Original length
= 0.42m – 0.38m
= 0.04 m
2.0N = k x 0.04m F k x
So, k = 2.0 N
0.04 m
= 50 N m-1

57. How much force would it take to stretch a steel bar with a spring constant of 21×106 N/m until it is 1.0mm longer?
what force would be required to compress a 20.cm long spring to 15cm if the spring constant is 30.N/m?
If a spring has a spring constant of 2 N/m and it is stretched 5 cm, what is the force of the spring?
What is the spring constant of a car spring if a 2500N force compresses it from a length of 50.cm to a length of 40.cm?
A spring is compressed 10m when a force of 5N is applied. How far does it compress when 10N is applied?
Peter (from Peter and the Wolf fame) is out hunting a possum with his spring loaded rock thrower. He pulls back on the spring with a force of 350 N and it stretches 10 cm. What is the spring constant?
A spring is 20cm long when a force of 10N hangs from it and 30cm long when a load of 20N hangs from it. What is the length of the spring a) with no load and b) when there is a load of 5N?
What mass, would cause a compression of 20cm when placed on top of the vertical spring with spring constant 30N/m?
A spring (k = 100 N/m) has a 1.2 kg mass on the end of the spring, how far does it stretch? If 300g are removed how far up does the remaining mass move? What mass would be required to stretch the spring 35 cm?

58. Elastic Limit OR Limit of proportionality
Elastic behaviour
Plastic behaviour

59. What is the elastic limit?
The material no longer shows elastic behaviour
-ie does not return to original size/shape when stretching force is removed
The material is permanently deformed
-i.e. is larger or longer than originally
The material is weaker as the above effects are
caused by fracture of some atomic bonds

60. What about energy stored?
When a spring is stretched it stores elastic energy.
This can be found from the area underneath the graph (before limit of proportionality has been reached this is a triangle)
Energy = Area = ½ base x height
= ½ xF
(and since we know F = kx)
Energy = ½ kx2