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Embed code for: 01 Describing Motion
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Distance is the length of the path travelled from one location to another
Distance from A to F is 3.5 km if travelled through the green path
Distance, time and speed
To work out the speed of an object, you need to know:
the distance travelled
how long it took to travel that distance.
Speed is the distance travelled during a unit time (a second, a minute or an hour) and is calculated using the following equation:
Speed can be measured in different units, e.g. m/s, km/h, km/s, miles per hour.
The units of distance and time will determine the units to be used for speed.
Words and units
Speed formula triangle
Speed calculation example
A girl takes 30 minutes to travel around a cross-country ski course, a distance of 18 km. Calculate her average speed in km/h.
distance (in km)
time (in h)
Converting units of speed
Let’s try to convert 10 km/h into m/s:
36 x 1000 m
1x 60x60 s
Speed calculation example – units
Now let’s calculate the speed of the girl in m/s.
distance (in m)
time (in s)
Supun sets off for a walk around the Tutor Wizard office at an average speed of 3.6 km/h. How far will he travel in 30 minutes?
Give your answer in km.
distance (km) = speed (km/h) × time (h)
= 3.6 km/h × 0.5 h
= 1.8 km
Time calculation – question 1
How long would it take for Supun to walk 500 m to the Office from the Thurstan Bus Stop, if his average speed was 1.1 m/s?
= 500 seconds
Average speed vs. instantaneous speed
The speed of a race car at any point or during a smaller time interval around a track is called the instantaneous speed. A car will have a different instantaneous speed at each of the points around the track.
Average speed is the total distance travelled divided by the total time taken. It is never bigger than the instantaneous speed.
Calculating average speeds
Unit of time
A unit of time is any particular time interval, used as a standard way of measuring or expressing duration.
The base unit of time in the International System of Units (SI), and by extension most of the Western world, is the second, defined as about 9 billion oscillations of the Caesium (Cs) atom.
To better understand how an object move it is better to look at its motion in smaller time intervals.
To graph the distance travelled by a car, let’s look at its motion in each second and note the distance after 5 second intervals
Observing motion of a car
Observed distances of the car
Calculating speed from the gradient
The slope of a graph is called the gradient.
The gradient of the line in a distance–time graph gives the speed
Simple graphs use straight lines only, making it easy to calculate the gradient.
It is difficult to calculate the gradient of ‘realistic’ graphs because the line is curved.
What’s the speed?
What is the speed of the object between points A and B?
the object has moved 60 m (70 – 10 )
it took 3 s to move this distance (6 – 3)
speed = distance/time
= 20 m/s
What’s the average speed?
How can we work out the average speed of this object between points C and D?
the object has moved 70 m (70 – 0 )
it took 9 s to move this distance (9 – 0)
= 7.8 m/s
Difference between Distance and Displacement
Distance refers to "how much ground an object has covered" during its motion.
Displacement refers to "how far out of place an object is"; it is the object's overall change in position.
Displacement = 5 km
Distance = 7 km
Scalers and Vectors
Scalars are fully described by a magnitude (or numerical value) alone
Vectors are fully described by both a magnitude and a direction. The direction of a vector is usually indicated by an arrow proportional to the magnitude.
Some times the arrows are drawn just to indicate the direction and the magnitude is mentioned alongside with the arrow
When you look at a moving object like a train, how do you identify if it is moving?
You have to compare the train’s position to another object, for instance the platform at the train station.
We cannot tell if something is moving unless we have something else to compare it to.
A train at a platform
If a train is not moving compared to the platform, the train is said to be at rest.
If the train starts to move and its position on the platform is changing, the train is in motion relative to the platform.
Relative means “compared to something else”. The train’s motion is relative to the station platform.
The platform is an object we use for comparison. It is called the reference point (or frame of reference).
Trains moving in the same direction
What if a red train is moving in the same direction as a yellow train at the same speed?
If you use the platform as your reference point, it looks like both trains are moving. Another way of saying this is “relative to the platform, both trains are in motion”.
What if you use the red train as your reference point instead?
In other words what if you’re looking at the yellow train sitting inside the red train?
The yellow train is travelling at the same speed as your reference point, so it would not change position. The yellow train would appear to be at rest!
When you state whether an object is at motion or at rest, you must say what your reference point is.
Trains moving in opposite directions (1)
What if the red and yellow trains are moving towards each other at the same speed?
If you use the platform as your reference point, it looks like both trains are moving towards the platform at the same speed.
Relative to the platform, both trains are in motion.
Trains moving in opposite directions (2)
What happens if you use the red train as your reference point?
The yellow train is moving towards the red train at the same speed as the red train is moving towards the yellow train.
Therefore, the yellow train appears to be in motion and it also appears to be travelling at an even greater speed. This is because the trains are moving at the same speed but in opposite directions.
So when you state whether an object is in motion or at rest, you must also think about which direction the object and the reference point are moving.
How is velocity different to speed?
The speed of an object does not depend on the direction in which it is travelling. Since velocity is a vector quantity the velocity of an object is its speed in a particular direction.
The direction could be north, south, east or west.
We can also assign a direction by making the object’s direction positive and the opposite direction negative (or vice-versa).
The speed of the car is 15 m/s.
The velocity of the car is +15 m/s.
Relative velocity calculations (1)
Two trains are moving on parallel tracks in the same direction. The red train is moving at +15 m/s. The yellow train is moving at +20 m/s.
What is the velocity of the yellow train relative to the red train?
The relative velocity is the difference between the velocity of the object in question (the yellow train) and the velocity of the reference point (the red train).
relative velocity = velocity of object – velocity of reference point
= velocity of yellow train – velocity of red train
= (+20) – (+15)
= +5 m/s
Relative velocity calculations (2)
Two trains are travelling at the same speed of 25 m/s on parallel tracks.
The red train has a velocity of +25 m/s. The yellow train has a velocity of –25 m/s. The signs (one positive and one negative) show that the trains are travelling in opposite directions.
What is the velocity of the red train relative to the yellow train?
= velocity of red train – velocity of yellow train
= (+25) – (–25)
= +50 m/s
Boardworks KS3 Science 2014
Describing Motion Worksheet One accompanies this slide. It has been designed to be used at any point in the presentation to help to reinforce how speed is calculated. This worksheet involves an outdoor activity.
Describing Motion Worksheet Three accompanies this slide.
Describing Motion Worksheet Two accompanies this slide.
The yellow train is travelling twice as fast relative to the first train.
To challenge more advanced students, ask them to work in teams to figure out the relative velocity in both scenarios.
Ask older or more advanced students to calculate the relative velocity of the red train compared to the yellow train. The red train’s relative velocity is –5 m/s.
Make sure students understand that there is a positive sign in front of the red train’s velocity even though positive signs aren’t always shown. To test their understanding of this concept, ask them what the relative velocity of the trains would be if the red train had a velocity of –25 m/s and the yellow train had a velocity of +25 m/s.
acceleration – An increase in speed.
average speed – The total distance travelled divided by the total time taken for a whole journey.
deceleration – A decrease in speed.
distance/time graph – A way of showing how an object moves using a graph.
instantaneous speed – The speed of an object at a particular moment.
metres per second – The unit of speed used in science. Distance must be measured in metres and time in seconds.
speed – How quickly an object is moving. It equals the distance moved divided by the time taken.
velocity – The speed and direction an object is travelling.
Describing Motiony of the object in question (the yellow train) and the velocity of the reference point (the red train).