2. 21/03/2024
Vector vs. scalar
Scalar quantities have size (“magnitude”) only and no direction.
Vector quantities have both size and direction.
Scalar or vector???
Scalar Vector
1. Mass
2. Distance
3. Displacement
4. Speed
5. Velocity
6. Energy
8. Power
7. Time
9. Momentum
10. Current
11. Force
12. Acceleration
3. 21/03/2024
21/03/2024
Speed vs. Velocity
Speed is simply how fast you are travelling…
Velocity is “speed in a given direction”…
This car is travelling at a
speed of 20m/s
This car is travelling at a
velocity of 20m/s east
5. 21/03/2024
21/03/2024
Distance, Speed
and Time revision
Speed = distance (in metres)
time (in seconds)
D
T
S
1) Oli walks 200 metres in 40 seconds. What is his speed?
2) Ella covers 2km in 1,000 seconds. What is her speed?
3) How long would it take Grace to run 100 metres if she
runs at 10m/s?
4) Alex runs to the shop to buy the new Fallout game and
travels at 50m/s for 20s. How far does he go?
5) Jasmine drives her car at 85mph (about 40m/s). How
long does it take her to drive 20km?
5m/s
2m/s
10s
1000m
500s
You need to learn this equation!!
6. 21/03/2024
21/03/2024
Distance, Speed and
Time (slightly harder!)
Speed = distance (in metres)
time (in seconds)
D
T
S
1) Matilda walks 2000m in 50 minutes. What is her speed in
m/s?
2) James tries to walk the same distance at a speed of 5m/s.
How long does he take?
3) Greg drives at 60mph (about 100km/h) for 3 hours. How
far has he gone?
4) The speed of sound in air is 330m/s. Evie shouts at a
mountain and hears the echo 3 seconds later. How far
away is the mountain? (Careful!)
0.67m/s
400s
300km
495m
8. 21/03/2024
21/03/2024
40
30
20
10
0
20 40 60 80 100
1) What is the speed during the first 20 seconds?
2) How far is the object from the start after 60 seconds?
3) What is the speed during the last 40 seconds?
4) When was the object travelling the fastest?
Distance
(metres)
Time/s
0.5m/s
40m
1m/s
40-60s
9. 21/03/2024
Distance-Time graphs
Task: Produce a distance-time graph for the following
journey:
1) Charlie walks 50m in 20 seconds.
2) She then stands still for 10 seconds
3) She then runs away from Harry and covers 100m in 30
seconds.
4) She then stands still and catches her breath for 20
seconds.
5) She then walks back to the start and covers the total 150m
in 50 seconds.
10. 21/03/2024
40
30
20
10
0
20 40 60 80 100
1) Who was travelling the fastest?
2) Who was travelling the slowest (but still moving)?
3) Who didn’t move?
Distance
(metres)
Time/s
G B
N
Y
11. 21/03/2024
40
30
20
10
0
20 40 60 80 100
1) What was the velocity in the first 20 seconds?
2) What was the velocity between 20 and 40 seconds?
3) When was this person travelling the fastest?
4) What was the average speed for the first 40 seconds?
Distance
(metres)
Time/s
1.5m/s
0.5m/s
80-100s
1m/s
12. 21/03/2024
Distance-time graph for changing speeds
40
30
20
10
0
20 40 60 80 100
Distance
(metres)
Time/s
Object is
speeding up
here Object is
slowing down
here
13. 21/03/2024
21/03/2024
Acceleration
V-U
T
A
Acceleration = change in velocity (in m/s)
(in m/s2) time taken (in s)
1) A cyclist accelerates from 0 to 10m/s in 5 seconds.
What is her acceleration?
2) A ball is dropped and accelerates downwards at a rate of
10m/s2 for 12 seconds. How much will the ball’s velocity
change by?
3) A car accelerates from 10 to 20m/s with an acceleration
of 2m/s2. How long did this take?
4) A rocket accelerates from 1,000m/s to 5,000m/s in 2
seconds. What is its acceleration?
2m/s2
120m/s
5s
2000m/s2
You need to learn this equation!!
14. 21/03/2024
21/03/2024
Acceleration V-U
T
A
Acceleration = change in velocity (in m/s)
(in m/s2) time taken (in s)
1) Mikey accelerates from standstill to 50m/s in 25 seconds.
What is his acceleration?
2) Jack accelerates at 5m/s2 for 5 seconds. He started at
10m/s. What is his new speed?
3) Rob is in trouble with the police. He is driving up the A29
and sees a police car and brakes from 50m/s to a standstill.
His deceleration was 10m/s2. How long did he brake for?
4) Another boy racer brakes at the same deceleration but only
for 3 seconds. What speed did he slow down to?
2m/s2
35m/s
5s
20m/s
15. Another equation of motion
21/03/2024
For a constantly-accelerating body, we can also use this
equation:
v2 – u2 = 2ax
1) An object starts from rest and accelerates at
a rate of 2m/s2 over a distance of 20m. What
is its final velocity?
2) Steve drives up the M1 and covers 30km. He
started at 2m/s and constantly accelerated
during the whole journey at a rate of
0.001m/s2. What was his final speed?
3) (Harder!) Sarah decelerates from 30 to 10m/s
over a distance of 5m. What is her
acceleration?
80m/s
64m/s
-80m/s2
17. 21/03/2024
21/03/2024
80
60
40
20
0
1) How fast was the object going after 10 seconds?
2) What is the acceleration from 20 to 30 seconds?
3) What was the deceleration from 30 to 50s?
4) How far did the object travel altogether?
10 20 30 40 50
Velocity
m/s
T/s
40m/s
2m/s2
3m/s2
1700m
18. 21/03/2024
21/03/2024
80
60
40
20
0
1) How fast was the object going after 10 seconds?
2) What is the acceleration from 20 to 30 seconds?
3) What was the deceleration from 40 to 50s?
4) How far did the object travel altogether?
10 20 30 40 50
Velocity
m/s
T/s
10m/s
4m/s2
6m/s2
1500m
21. 21/03/2024
Different Ways of
measuring Speed
After 0s After 1.5s
Example 1 - Speed cameras work by recording the
position of the car at a certain time apart. What
is the speed of the trolley in the lab example
done below?
22. Different Ways of Measuring
Speed
21/03/2024
Example 2 – Using Light Gates
To a
computer/
data logger
23. Speed
21/03/2024
Speed is a scalar quantity. What does this mean?
Typical values for speed:
Walking ≈ 1.5m/s
Running ≈ 3m/s
Cycling ≈ 6m/s
What about cars? Aeroplanes?
24. 21/03/2024
Acceleration due to Gravity
If I throw this ball upwards with a speed of 40m/s
why does it come back down again?
The ball is acted on by a force called gravity,
which accelerates the ball downwards at a rate
of 10m/s2 near the Earth’s surface.
Extension question – how far up would the ball go?
1) Take u = 40m/s and v = 0m/s (at the top of the
throw)
2) Take a = 10m/s2
3) Therefore s = 80m
v2 – u2 = 2ax
25. Approximate Accelerations
21/03/2024
Which approximate values of speed, acceleration and force
would you put with these moving objects?
Speed = 30m/s
Speed = 1.5m/s
Speed = 300m/s
Acceleration = 1.5m/s
Acceleration = 2m/s
Acceleration = 3m/s
Force = 70N
Force = 3000N
Force = 600,000N
26. 21/03/2024
21/03/2024
Balanced and unbalanced forces
Consider a camel standing on a road.
What forces are acting on it?
Weight
Reaction
These two forces would be equal –
we say that they are BALANCED.
The camel doesn’t move anywhere.
27. 21/03/2024
21/03/2024
Balanced and unbalanced forces
What would happen if we took the
road away?
Weight
Reaction
The camel is acted on by an
“unbalanced force”, which
causes it to accelerate. This is
called Newton’s 1st law of
motion.
28. 21/03/2024
Newton 1642-1727
Newton’s 1st Law of Motion
Basically, a body will remain at rest or
continue to move with constant velocity as
long as the forces acting on it are balanced.
An unbalanced forwards
force will make me
accelerate…
…and an unbalanced
backwards force will make
me slow down…
30. 21/03/2024
21/03/2024
Balanced and unbalanced forces
1) This animal is either
________ or moving
with _______ _____…
4) This animal is also
either _______ or moving
with ________ ______..
2) This animal is getting
________…
3) This animal is getting
_______….
Words - Stationary, faster, slower or constant speed?
31. 21/03/2024
21/03/2024
Summary of Newton’s 1st law
If an object is stationary and has NO resultant force on it the object
will…
If an object is stationary and a resultant force acts on it the object will…
If an object is already moving and NO resultant force acts on it the
object will…
If an object is already moving and a resultant force acts on it the object
will…
Complete these sentences…
…continue to stay stationary …accelerate in the direction of the
resultant force
…continue to move at the same
speed and the same direction
…accelerate in the direction of the
resultant force
32. 21/03/2024
Newton’s 2nd Law of Motion
Newton 1642-1727
The acceleration of a body is proportional to
the resultant force causing its acceleration
and is in the same direction. It is inversely
proportional to the mass of the object.
In other words…
force = mass x acceleration F
A
M
You need to learn this equation!!
33. 21/03/2024
21/03/2024
Force, mass and acceleration
1) A force of 1000N is applied to push
a mass of 500kg. How quickly does
it accelerate?
2) A force of 3000N acts on a car to
make it accelerate by 1.5m/s2. How
heavy is the car?
3) A car accelerates at a rate of
5m/s2. If it weighs 500kg how
much driving force is the engine
applying?
4) A force of 10N is applied by a boy
while lifting a 20kg mass. How
much does it accelerate by?
F
A
M
2m/s2
2000kg
2500N
0.5m/s2
34. More information about Weight
21/03/2024
1) How much does 1kg weigh on the Earth?
2) How much does 2kg weigh?
3) How much does 3kg weigh?
4) What are you noticing about your answers?
Whatever mass goes up by, weight goes up by the same ratio.
For example, if you double mass you double weight. This is
called “proportionality”:
35. 21/03/2024
21/03/2024
Weight vs. Mass
Earth’s Gravitational Field Strength is 10N/kg. In other
words, a 1kg mass is pulled downwards by a force of 10N.
W
g
M
Weight = Mass x Gravitational Field Strength
(in N) (in kg) (in N/kg)
1) What is the weight on Earth of a book with mass 2kg?
2) What is the weight on Earth of an apple with mass 100g?
3) Charles weighs 700N on the Earth. What is his mass?
4) On the moon the gravitational field strength is 1.6N/kg.
What will Charles weigh if he stands on the moon?
20N
1N
70kg
112N
You need to learn this equation!!
36. 21/03/2024
Testing Newton’s 2nd Law
For the experiment:
1) Draw a diagram of how you set it up
2) Describe your method
3) Describe what equipment you used to get the results and
how you analysed them.
38. 21/03/2024
Centripetal Force (HT only)
Why does this ball keep moving
in a circle?
In order to keep an
object moving in a circle a
resultant force needs to
be applied and this force
always goes towards the
centre of the circle.
This is called a “centripetal force”
39. Examples of Centripetal Force
21/03/2024
What is the centripetal force
in each of these situations?
40. Inertial Mass (HT only)
21/03/2024
Newton 1642-1727
Inertial mass is a measure of how difficult it is
to change the velocity of an object:
Inertial mass = force / acceleration
Determine the initial mass of the following:
1) A car that needs a force of 2000N to
accelerate it by 1m/s2.
2) A bus that accelerates at a rate of
0.5m/s2 when 5 people push it, each with
a force of 750N.
2000kg
7500kg
41. 21/03/2024
Newton’s 3rd Law of Motion
Newton 1642-1727
When body A exerts a force on body B, body
B exerts an equal and opposite force on body
A.
My third law says
that if I push to
the right I will
move backwards
as well.
43. 21/03/2024
21/03/2024
Momentum
Any object that has both mass and
velocity has MOMENTUM. Momentum
(symbol “p”) is simply given by the formula:
Momentum = Mass x Velocity
(in kgm/s) (in kg) (in m/s)
P
V
M
What is the momentum of the following?
1) A 1kg football travelling at 10m/s
2) A 1000kg car travelling at 30m/s
3) A 0.02kg pen thrown across the room at 5m/s
4) A 70kg bungi-jumper falling at 40m/s
10kgm/s
30,000kgm/s
0.1kgm/s
2800kgm/s
You need to learn this equation!!
44. 21/03/2024
21/03/2024
Conservation of Momentum
In any collision or explosion momentum is conserved (provided that there
are no external forces have an effect). Example question:
Two cars are racing around the M25. Car A collides with the back of car B
and the cars stick together. What speed do they move at after the
collision?
Mass = 1000kg Mass = 800kg
Speed = 50m/s Speed = 20m/s
Momentum before = momentum after…
…so 1000 x 50 + 800 x 20 = 1800 x V…
…V = 36.7m/s
Mass = 1800kg Speed = ??m/s
45. 21/03/2024
21/03/2024
Momentum in different directions
What happens if the bodies are moving in opposite directions?
Speed = 50m/s
Mass = 1000kg
Speed = 20m/s
Mass = 800kg
Momentum is a VECTOR quantity, so the momentum of the
second car is negative…
Total momentum = 1000 x 50 – 800 x 20 = 34000 kgm/s
Speed after collision = 34000 kgm/s / 1800 = 18.9m/s
46. 21/03/2024
21/03/2024
Another example
Consider the nuclear decay of Americium-241:
Am
241
95
α
4
2
If the new neptunium atom moves away at
a speed of 5x105 m/s what was the speed
of the alpha particle?
Np
237
93
2.96x107 m/s
47. 21/03/2024
21/03/2024
More questions…
1. A car of mass 1000kg heading up the M1 at 50m/s collides
with a stationary truck of mass 8000kg and sticks to it.
What velocity does the wreckage move forward at?
2. A defender running away from a goalkeeper at 5m/s is hit
in the back of his head by the goal kick. The ball stops
dead and the player’s speed increases to 5.5m/s. If the
ball had a mass of 500g and the player had a mass of 70kg
how fast was the ball moving?
3. A white snooker ball moving at 5m/s strikes a red ball and
pots it. Both balls have a mass of 1kg. If the white ball
continued in the same direction at 2m/s what was the
velocity of the red ball?
4. A gun has a recoil speed of 2m/s when firing. If the gun
has a mass of 2kg and the bullet has a mass of 10g what
speed does the bullet come out at?
5.6m/s
70m/s
400m/s
3m/s
48. 21/03/2024
21/03/2024
Recap question on momentum
1. Bradley and Jack are racing against each other over 400m
at Sports Day. Brad is running at 8m/s and catches up with
Jack who is running at 6m/s. After the collision Brad stops
and Jack moves slightly faster. If Brad’s mass is 60kg and
Jack’s is 70kg calculate how fast Jack moves after the
collision.
2. Coryn is driving her 5kg toy car around. It is travelling at
10m/s when it hits the back of Shannon’s (stationary) leg
and sticks to it. Assuming Shannon’s leg can move freely
and has a mass of 10kg calculate how fast it will move after
the collision.
12.9m/s
3.3m/s
49. 21/03/2024
Change in Momentum and Force
Instead of F=ma Newton actually said that the force acting on
an object is that object’s rate of change of momentum. In
other words…
mv-mu
T
F
Force = Change in momentum
Time
(in N)
(in kgm/s)
(in s)
For example, Rob Stocker scores from a free kick by kicking a stationary
football with a force of 40N. If the ball has a mass of 0.5kg and his
foot is in contact with the ball for 0.1s calculate:
1) The change in momentum of the ball (its impulse),
2) The speed the ball moves away with
You DON’T need to learn this
equation!!
50. 21/03/2024
Example questions
1) Jack likes playing golf. He strikes a golf ball with a
force of 80N. If the ball has a mass of 200g and the
club is in contact with it for 0.2s calculate a) the change
in momentum of the golf ball, b) its speed.
2) Chad thinks it’s funny to hit tennis balls at Illy. He
strikes a serve with a force of 30N. If the ball has a
mass of 250g and the racket is in contact with it for
0.15s calculate the ball’s change in momentum and its
speed.
3) Oli takes a dropkick by kicking a 0.4kg rugby ball away
at 10m/s. If his foot was in contact with the ball for 0.1
seconds calculate the force he applied to the ball.
4) Paddy strikes a 200g golf ball away at 50m/s. If he
applied a force of 50N calculate how long his club was in
contact with the ball for.
16kgm/s,
80m/s
4.5kgm/s,
18m/s
0.2s
40N
51. 21/03/2024
Measuring Reaction Times
For the experiment:
1) Describe your method (i.e. how will you measure reaction
time?)
2) Describe what you are varying (your “independent variable”)
3) Describe what equipment you used to get the results and
how you analysed them.
Typical reaction times are around 0.4
to 0.9s. How did you compare?
54. 21/03/2024
21/03/2024
Stopping a car…
Braking
distance
Too much
alcohol
Thinking
distance
(reaction time)
Tiredness
Too many
drugs
Wet roads
Driving too
fast
Tyres/brakes
worn out
Icy roads
Poor
visibility
Total Stopping Distance = Thinking Distance + Braking Distance
55. 21/03/2024
21/03/2024
Stopping a car…
What happens inside the car when it stops?
In order to stop this car the
brakes must “do work”. This work
is used to reduce the kinetic
energy of the vehicle and the
brakes will warm up.
Greater speed =
greater force
needed to stop in a
given distance =
hotter brake pads!
56. 21/03/2024
21/03/2024
Forces and Deceleration
What is the deceleration of these objects?
A skydiver when he
opens his parachute
A formula 1 car
about to take a
sharp turn
A car slowing down
at traffic lights
300m/s2
10m/s2 40m/s2
Q. What happens to the human body when these forces get
TOO big?
57. Approximate Forces (HT only)
21/03/2024
Which approximate values of speed, acceleration and force
would you put with these moving objects?
Speed = 30m/s
Speed = 1.5m/s
Speed = 300m/s
Acceleration = 1.5m/s
Acceleration = 2m/s
Acceleration = 3m/s
Force = 70N
Force = 3000N
Force = 600,000N
59. 21/03/2024
Stopping Distances
This diagram (taken from drivingtestsuccess.com) shows the thinking and
braking distances for different speeds. What patterns do you notice?
Thinking distance increases
linearly
Braking distance increases in
a squared relationship
