Motion
LESSON OBJECTIVES
• To understand distance against time graphs
• To calculate average speeds
Keywords: distance, speed, time,
gradient
What is speed?
Speed is a measure of how far an object moves in a
given time.
This car is travelling at 60
mph. This means the car
travels 60 miles every
hour.
This jet is travelling at
350 m/s. This means the
jet travels 350 metres
every second.
How is speed calculated?
speed =
distance travelled
time taken
● Distance travelled is measured in metres (m).
● Time taken is measured in seconds (s).
● Speed is measured in metres per second (m/s).
The standard unit for speed in physics is m/s, but
other units such as kilometres per hour (km/h) are
more convenient when measuring the speed of
vehicles. Why is this?
Calculating speed question
A train takes 100 seconds to travel 1,500 m. What is the speed of the
train?
distance
time
speed =
= 1,500
100
= 15 m/s
Using a Formula Triangle
Questions
÷
÷
x
s =
d
t
1. If a person is walking at 3m/s
for 5 seconds how far will
they have walked?
2. A student runs 100m in 15
seconds, how fast was she
running?
3. A bike travels at 10m/s and
goes 1000m, how long was it
travelling for?
4. A can takes half an hour to
travel 1000m, what speed
was it travelling at?
Speed, distance, time calculations
Distance / Time graphs
• How fast is a maggot?
• Record your results in a table.
• Plot a LINE graph to show your
results.
• The GRADIENT of the line
graph is the maggots speed.
Who has the fastest maggot?
Making a Distance against Time
graph
• You can watch someone moving, and fill out a table
like this:
Distance
(m)
0
10
20
30
40
50
60
70
Time (S)
0
5
10
10
10
20
30
40
• Then plot the graph.
What is happening?
Distance against Time graph for
student walking in classroom.
Distance
Moving
Fast
Standing
Still
Moving
Slowly
Time
Motion Sensor
• This is easier to use.
• It sends out a click.
• The click travels to the object
• It reflects back.
• The computer senses how long this takes.
• Then calculates a distance.
• Just like how bats “see” using echo sounding.
Using The Motion Sensor
• See if you can match the shapes
• What did the graph look like when the person was;
• standing still
• moving fast
• Moving slowly
• Why did the person hold a piece of paper?
Speed from Graphs
• To tell what speed an object is travelling at from a
graph, you need to look at the slope.
• The steeper the slope, faster the object is
travelling.
What’s the speed?
• What is the speed of the object between points A and B?
70
B
● the object has moved 60 m
(70 - 10 )
distance (m)
60
50
● it took 3 s to move this distance
(6 - 3)
40
30
● speed = distance/time
20
A
= 60/3
10
= 20 m/s
0
0
1
2
3
4
5
time (s)
6
7
8
9
Questions
A sprinter ran in a 100 m race. The graph
shows what happened:
a) What was the runner’s time for the 100 m
race?
b) Calculate the runner’s average speed for the
race.
c) Describe how the runner’s speed was
changing at each of the points A, B, C, D.
d) At which point was the speed greatest?
Explain your choice.
e) What distance was needed to stop at the end
of the race?
What is the speed?
• Estimate the average speeds for the following
things (in m/s)
•
•
•
•
•
•
A car on the motor way
Light
300 000 000 m/s
Sound
330 m/s
An aeroplane
An Olympic 100m runner 250 m/s
The moon travelling around the Earth
31 m/s
10 m/s
1000 m/s
Using a Formula Triangle
÷
÷
x
s =
d
t
Questions
1.
My mom is walking at 10 m/s for 30
seconds how far will she have walked?
2.
Wesley runs 200m in 35 seconds, how
fast was he running?
3.
A train travels at 300m/s and goes
9000m, how long was it travelling for?
4.
A skateboarder takes an hour and a
half to travel 1600m, what speed was
he travelling at?
Velocity Time Graphs
LESSON OBJECTIVES
• To understand and interpret Velocity against Time
graphs
• To calculate acceleration.
Velocity Time Graphs
LESSON OBJECTIVES
• State the difference between speed and velocity
• To understand Velocity against Time graphs
• To calculate acceleration
Velocity and speed
• Remember from last lesson
s =
d
t
• When a car is travelling at 10m/s, it is travelling in a certain
direction (North, south etc.)
• VELOCITY is speed in a given
direction
How is velocity different to speed?
The speed of an object does not depend on the direction in which it is travelling. The
velocity of an object is the speed and direction in which it is moving.
The car is
travelling north
with a velocity
of 10 m/s.
As the car goes round
the corner, the speed of
the car remains
constant but the
velocity changes.
What does this graph mean?
Velocity against Time graph for
student walking in classroom.
Velocity
Travelling at a
steady
velocity
Getting
faster
Getting
Slower
Time
Not
Moving
Recreating Graphs
• The motion sensor we used before can take a
distance time graph and calculate a velocity time
graph.
• How does it do this?
Velocity
• The velocity of an object is its
speed in a particular direction.
• This means that two cars
travelling at the same speed, but
in opposite directions, have
different velocities.
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.
The brakes on this
motorcycle are causing it
to slow down. This is
negative acceleration or
deceleration.
Sketch a graph to show
this motion…..
Consider a train
accelerating from rest to a
top speed of 100m/s in a
time of 5s. It then
remains at a constant
speed for 10s before
decelerating at the same
rate and coming to rest.
How is acceleration calculated?
The acceleration of an object can be calculated using this equation:
acceleration =
change in speed
time taken
● Change in speed 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).
Using a formula triangle
A formula triangle helps you to rearrange a formula. The formula triangle for
acceleration (a), speed (s) and time (t) is shown below.
Cover the quantity that you are trying to work out, which gives the
rearranged formula needed for the calculation.
So to find acceleration (a),
cover up a…
…which gives the
formula…
÷
÷
x
a =
s
t
A racing car accelerates from rest to a speed of 60 m/s in
a time of 4 seconds. What is the acceleration of the car?
acceleration =
=
change in speed
time taken
60
4
= 15 m/s2
A hungry cheetah spots a gazelle and decides to chase it.
The cheetah accelerates at 10 m/s2 from rest until it
reaches 20 m/s. How long did this take?
change in speed
time taken
acceleration =
change in speed
acceleration
time taken =
=
= 2s
20
10
Acceleration questions
1.
A car has a constant acceleration of 4 m/s2, starting from rest. How
fast is it travelling after 5 seconds?
1.
A sports car accelerates from rest at 4 m/s2 for 10 seconds.
Calculate the final velocity.
1.
How long does it take for a car to change its velocity from 10 m/s to
25 m/s if the acceleration is 5 m/s2?
1.
A baseball thrown at 25.0 m/s strikes a catcher’s mitt and slows
down to rest in 0.500 s. What is the magnitude of the ball’s
acceleration?
1.
A hockey puck travelling at 10.0 m/s strikes the boards, coming to
rest in 0.0300s. What is the magnitude of the puck’s acceleration?
Velocity-time graphs
What does the gradient show in this case?
20 40 60 80 100
Velocity m/s
The area under the graph is also important as it
represents the distance travelled.
Use the graph to
calculate the
acceleration of the
train. And the total
distance travelled.
5
10
15
20
Time /s
Question
The blue line
shows the
movement of a
blue car and
the red line
shows the
movement of a
red car.
Use the graph
to find the
acceleration
and distance
travelled for
each of the
cars.
Using velocity time graphs to find
the
distance
travelled
• The whole area under the
velocity-time graph
represents the distance
travelled
• You need to find the total
area under the line
• How do you work out the area
of a triangle?
• ½ x height x its base
• How do you work out the area
of a rectangle?
• height x base
• Add them both together to
give you the total distance
travelled
Speed bumps
• Speed bumps on a road are intended to stop drivers
speeding. Anyone in a vehicle that crosses a speed
bump too fast will experience an uncomfortable jolt.
In this investigation, your task is to record the motion
of a model car as it travels across two model ‘speed
bumps’.
Investigation
Below are two different types of speed bumps but which
is the best? The idea is to reduce the cars speed as much
as possible. Which shape and size of speed bump is the
best?
Method
• Design and build two different types of speed bumps to test.
These will be secured to the runway.
• Cut the tape to the required length and attach the tape to the
back of the trolley.
• Do a practice run as a control to give you something to compare
your results to.
• When you have your control you can place your speed bumps
on the runway and record how the motion is altered.
Practical
The closer together
the dots are the
slower the vehicle is
moving.
If they are getting
further apart, the
vehicle is accelerating if
they get closer together
it is decelerating.
Analysis
When you have your ticker tape sample you
need to cut it into strips which are 5 dots
long. Stick the strips in order onto graph
paper so that it looks like the image shown
You may not need the first few but locate
where the vehicle hit the bumps and
examine their effect of it’s motion.
You should be able to tell which type
had the biggest effect on the motion.
Motion Represented on Graphs.
There are two types of motion graphs, and three
types of motion. Best represented in a table.
Distance/Time
Stopped
V
150
t
Const’
Velocity
Velocity Time Graph for parachutist.
Velocity/Time
D
Question
V (m/s)
t
15
D
V
T (s)
15
50
100
A. What was his acceleration from 0 to 15 sec ?
t
Const’
Accel’n
t
D
V
B. What was happening at 50 seconds?
He had just opened his parachute and was
decelerating.
t
Gradient = Velocity
t
C. Approximately how far did he fall altogether?
Gradient = Accel’n
Area = Distance
Area under graph ≈ 50 × 150 + 50 × 15 = 8250m
travelled
Recap
Area
Distance vs
Time Graphs
Velocity vs
Time Graphs
Gradient
Acceleration
Gradient
Motion Graphs
• Look at each card.
• Describe the motion for each graph
• Calculate the distance/velocity/acceleration HT