Describing Motion

The AQA KS3 Specification states "If the overall, resultant force on an object is non-zero, its motion changes and it slows down, speeds up or changes direction."

If you have worked through the KS3 Contact Forces page you will understand the meaning of "Resultant Force" as well as the terms "Balanced Forces" and "Unbalanced Forces". What we need to do here is to understand how we describe these changes in motion.

In particular, how to describe:
Slowing down
and Speeding up

To do this we will make use of a few words which have very precise meanings; these words are DISTANCE, SPEED and ACCELERATION.

1. Distance

Distance is how far an object moves.

So, if an athlete runs 100m in a straight line, the "Distance" is 100m; if another athlete runs all the way round the oval track then he/she will have run a distance of 400m.

In either case, the fact that one athlete ran in a straight line whilst the other ran in an oval (and ended up back at the start) was irrelevant as far as Distance was concerned.

So, what we are saying is, is that a Distance measurement takes no account of the direction travelled.

For a Distance measurement the only thing that matters is how far the object has moved and we measure it in metres, m.

2. Speed

Speed is how much distance is covered in how much time.

Or Speed is the distance travelled divided by the time taken.

This leads us straight into the formula for Speed, which is:

Now although its not a requirement of the KS3 Specification, your teacher might wish you to be able to re-arrange the Speed formula in order to use it to calculate the distance travelled ! If so, this is what you would do.

So, let's do another example calculation, but this time we will calculate a distance travelled.

Relative Motion

Have you ever sat on a train and looked out of a window at a train next to you and then after many seconds realised that your train was moving, but so was the other one! Both trains moved off at the same time and at the same speed and in the same direction such that it appeared to you that both were stationary.
Eventually your train picks up speed and slowly pulls away from the other train; relative to the other train your train is moving slowly even though relative to the land it might be moving very fast.

We call this "relative motion". We also notice it when we (as the observer) look across from one car to another when pulling off from traffic lights; our car appears stationary "relative to" the nearby car.
But when we drive towards and past an approaching car it seems that we pass each other at a high speed; in this situation, the speed "relative to" an observer in one of the cars is the sum of the individual speeds (this is why head on collisions of vehicles are the worst and often deadly).

Typical Personal Speed Values:

1. Walking 1.5m/s
2. Running 3m/s
3. Cycling 6m/s

All of these values will vary with age and fitness of the person and the state of the terrain, eg hilly or muddy compared to smooth, level tarmac. Also, it is obvious that a person's speed varies during a walk or a run or a ride, so these values are only average values. NB. When speed varies over a period of time, we call that period of motion, non-uniform motion.

Other forms of transportation can have much higher average speeds eg a car could have a speed between 13 and 31m/s, whilst a jet airplane can cruise at over 200 m/s.

Sound travels faster than all of these things. It has a typical speed of 330m/s in air (it travels even faster through water and faster still through solids! You can find out those values yourself.)

Describing Motion using Distance-Time Graphs

Distance-time graphs such as the one shown below can be used to describe the motion of an object travelling in a straight line and in particular to calculate the speed of an object at various points on its journey.

Since Speed = Distance / Time , the Gradient of the line on the Distance-time graph reveals the speed of the object.

The graph above is the simplest Distance-time graph since it shows just a single slope (or gradient) line. This will tell us about just one speed of the object.

Let's calculate the speed of the object revealed by this graph.

More complex graphs will have multiple slopes and can tell us how the speed of an object changes during its journey.

The second graph, below, is a more complex one showing multiple slopes which will reveal multiple speed values.

Graph 2: Three slopes (including the flat section) reveal three speeds.

Let's consider another graph. Look at the 3rd graph.

Graph 3: Four slopes reveal four speed values.

The main difference compared to the first two graphs is that it has a section with a negative slope. What does this signify? It simply means that the object has turned around and is heading back towards its starting point (the distance is getting less as time increases, reaching 0m, the starting point, at 100s). But since it is including direction information, the Y-axis label on the graph has been changed to Displacement.

NB Strictly speaking "Displacement" is not part of KS3, but of KS4 so feel free to skip over this example.

So, the calculations for graph 3 are the same as for graph 2 but with one extra section:

So far, so good. But what would the Distance-time graph mean if the "lines" were not straight but were curved?

Look at the fourth graph.

The "line" is now curved! What does it mean?

The slope or gradient gets steeper and steeper as time increases. So, this object is getting faster and faster as time increases. The object is speeding up; it is accelerating.

So a curved "line" on a Distance-time graph means that an object is accelerating.

3. Acceleration

As we stated above, when an object "speeds up", it is accelerating

Acceleration can be defined as how quickly the speed of an object increases or decreases.

The greater the change of speed or the smaller the time taken for the change to take place, the larger the acceleration of the object.

Now, the KS3 Specification does NOT require you to know how to CALCULATE acceleration, but it is not difficult since it follows directly from the above definitions, so we are going to have a go!

The definitions lead to this formula for acceleration:

The Effect of a Changing Force on an Object's Speed

Look at the diagram of the car below.

It is moving at a constant speed of 2 m/s and because of this it is in a state of equilibrium
(meaning that any forces acting on it are balanced so the overall or resultant force acting on it is zero, OK? If you don't get this you need to read 3.1.3Contact Forces ).

Now, all of a sudden, the engine force increases by 7N but so does the air resistance force. See the second diagram.

What will happen to the speed of the car?

Since the forces are still balanced, the resultant force is still zero, the car remains in its state of equilibrium, so there is NO CHANGE to the speed of the car!

In the third diagram, the driver has taken her foot off the accelerator causing the engine force to decrease, as you can see.

Now there is a backwards resultant force of 3N.
What will this do to the speed of the car?
First of all, since there is a resultant force then there will be a CHANGE. And the change will be in the direction of the resultant force, so the car will slow down. It Decelerates.

Finally, the driver presses the accelerator pedal down increasing the forward force such that it is greater than the air resistance force, as you can see in the fourth diagram.

Now there is a forward resultant force of 3N.
What will this do to the speed of the car?
This time the CHANGE will be in the forward direction, in the direction of the resultant force, meaning that the car will speed up. It Accelerates.

The Effect of the size of a Resultant Force on an Object's Acceleration

We have already made it clear and simple: A resultant force causes an acceleration.

The last thing to think about is the link between the size of the resultant force and the size of the acceleration that it produces.

Luckily, the link is very obvious:

If you don't follow this then you really need to read 3.1.3_Contact Forces first!