Objectives:

• To understand the terms displacement, instantaneous speed, average speed, velocity and acceleration

We can calculate the average speed of something moving if we know the distance it moves and the time it takes to travel that distance:

$v = \frac{d}{t}$

where;
$v$ is the average speed
$x$ is the distance traveled
$t$ is the time in which the object traveled for.

If the object is moving at a constant speed, this equation will give us the speed during the time taken, while if the speed is constantly changing, then the equation gives us its average speed, which is calculated over a period of time. If you look at the speedometer in a car, it doesn’t tell you the car’s average speed, instead it tells you its speed at the instant when you look at it. This is called the instantaneous speed.

Determining speed

You can find the speed of something moving by measuring the time it takes to travel between two fixed points. Using a stopwatch you can time a car over a distance. Note that this can only tell you the car’s average speed between the two points. You cannot tell whether it was increasing its speed, slowing down or moving at constant speed.

Using two light gates

When the moving object passes through a light gate, it interrupts the light beam as it passes. The timer starts measuring and it stops only when the object interrupts the light beam of the second light gate. The object’s speed is calculated from the time interval and the distance between the time gates.

Using one light gate

The timer starts when the start of the object breaks the light beam. It then stops when the end of the object passes through and the beam is not interrupted anymore. In this case, the time shown is the time taken for the object to travel a distance equal to the length of the object.

Using a ticker-timer

The ticker-timer machine marks a dot on a ticket paper (the tape) every $0.02 \ s$. This is due an alternating current, and the frequency of the alternating main is $50 \ Hz$ (This represent $50$ times per second and so the time between two ticks is $\frac{1}{50} \ seconds = 0.02 \ s$. The tape is attached to the moving objects and the pattern of dots acts as a record of the object’s movement.

If the spacing of the dots is constant then the object traveled at constant speed, if the spacing is increasing then the object was accelerating. Measure the distance of every fifth dot from the start, which will give you the distance traveled at intervals of $0.1 \ s$. Then plot a distance against time graph to see the motion of the object.

Speed and velocity

It is often important to know both the speed of an object and the direction in which it is moving. Speed and direction are combined in another quantity, called velocity. It is important to understand the difference. The velocity of an object can be thought of as its speed in a particular direction, so it is a vector quantity. Speed is the corresponding scalar quantity as it does not have a direction. So, to give the velocity of something, we have to state the direction in which it is moving.