Topic 1 - Motion

Speed, Velocity, and Acceleration

This topic looks at linear motion, i.e. motion in a straight line.

• Distance is how far you travel between any two points by any route.  It is a scalar quantity.

• Displacement is the minimum “as the crow flies” distance between two points.  It is a vector quantity, so it has direction.

• Speed is how fast you go, the rate of change of distance.

• Velocity is rate of change of displacement.  It must have a direction.

• Acceleration can be used as both a vector and a scalar quantity.  It is the rate of change of speed or velocity.

  You will be familiar with the simple equations:

            speed (m/s) = distance (m)        

                                    time(s)

            velocity (m/s) = displacement (m)

                                                time (s)

We also know acceleration as:

 The picture below shows the difference between distance and displacement.

Suppose we have two towns A and B 10 km apart but either side of a hill.  They are joined by a railway line that is straight, and goes through the hill in a tunnel.  The road goes round the hill and the total journey distance is 25 km.

So the distance is 25 km.  The displacement (the straight-line distance in a particular direction) between A and B is 10 km due East.

If we go from A to B and back again, the distance is 50 km, but the displacement is 0.

Information and Communication Technology (Computers) can be used to demonstrate the motion of a vehicle.  Sensors (light gates or ultrasonic detectors) are connected to a computer and the computer will record the data at time intervals.  The computer will plot a graph of the motion.

Click HERE to see some important definitions.

Graphical Interpretation of Acceleration

We can represent the movement of objects using a graph, usually plotting time on the x-axis (horizontal) and the speed or distance on the y-axis (vertical).

Consider a train accelerating from a station along a straight and level track to a maximum speed and slowing down to a stop at the next station.  The easiest way to show this is with a speed time graph.

Acceleration is the gradient of the speed-time graph.

From the graph,

• between O and A, the train is accelerating;

• between A and B, the train travels at a constant speed;

• between B and C, the train slows down.  Slowing down can also be called negative acceleration, or deceleration.  It is given a minus sign.

Distance is the area under the speed-time graph.  To work out the total distance, we would add the areas of:

• triangle OAX;

• rectangle ABXY;

• triangle BCY.

The corresponding distance time graph is like this:

We can work out the speed at any instant by measuring the gradient of the distance time graph. The curved line tells us that the speed is changing.

Acceleration is usually uniform, which means that the speed [velocity] is changing at a constant rate.    This is shown by a straight line on a speed time graph.  However in many real life situations acceleration is not constant.  Therefore the graph is not a straight line:

 Good graphical skills are important in Physics.  Click HERE if you need to review graphs.