Speed

From GCSE you will know that:

Average speed (m/s) = distance travelled (m) ÷ time taken (s)

In Physics Code:

The strange looking symbol D is "Delta", a Greek capital letter "D", which means "change in" or "difference in".

In the right direction

• Scalar quantities have a value.

• Vector quantities have both a value and direction.

The picture shows the difference between displacement and distance.  If you go from A to B to C, your distance is 65 metres, while your displacement is 35 metres to the right (direction given).  If you retrace your steps, the total distance is 130 m, while your displacement is zero, because you ended up in the place you started.

You need to know which quantities are vectors or scalars:

So:

Note that we can use vectors in the same sense as a scalar, in that we don't always have to state the direction.  Strictly speaking we ought to write the magnitude of the vector (but we don't, and it doesn't matter at this level).

Watch out for the following bear traps:

• Velocity is not a posh word for speed, although it's often used as that in exams.

• Make sure you are consistent with units.  Convert units if you need to.  If you're not sure, use SI units.

Acceleration

Acceleration is the rate at which the velocity increases:

 In Physics code:

or

This only works for uniform acceleration, i.e. constant acceleration.

Motion Graphs

We can represent motion using graphs:

• displacement-time;

• velocity-time;

• acceleration-time.

The time always goes on the horizontal axis.  Here are some displacement time graphs:

Graph (a) is where the velocity is constant.  It's a straight line.

Graph (b) has a velocity that is increasing.  We can tell this by looking at the gradient.  On a curved line, the gradient is the tangent at the point we are interested in.  We can easily see that the velocity is increasing.

Remember to use a big tangent as shown in the picture above.

The next pictures are of velocity time graphs.

Graph A shows constant velocity.

Graph (b) shows increasing velocity. 

The gradient tells us the acceleration.  The area under the graph gives us the displacement.

The acceleration time graph is shown below:

The area gives us the change in velocity.  At this level, we are only concerned with uniform acceleration.

Equations of Motion

There are four of these.  They use the following Physics Codes:

They are all derived from the velocity time graph.  Click on each link to see how:

In the exam you need to know which equation to choose.  This flow diagram will help you:

Force and Acceleration

Force is linked with mass and acceleration by the simple relationship:

F = ma

We can combine this equation with that for acceleration:

This gives us:

The force of gravitational attraction acting on a mass is called weight.  The relationship between mass and weight is given by:

F = mg

From this we can see that the term g is an acceleration, the acceleration due to gravity.  It has the value 9.81 m s^-2 and acts vertically downwards.  The approximation 10 m s^-2 is often used.