## Uniformly Accelerated Motion

If the acceleration of a body is uniform or constant, simplifications become possible so it is important to determine if the acceleration is uniform to a good approximation.

Possible methods of finding if the acceleration of a body is uniform include:

Light gates – a light gate is a device that detects when a body is passing because a light beam is interrupted by that passing body. The time for a body to pass between two point is thus recorded. If the length of the object that breaks the beam is recorded, the average initial speedthrough the first gate, the final speedthrough the second gate and the time t to travel from the first to the second gate can be found. The acceleration is then found from the equation

Strobe lights – A strobe light flashes at fixed time intervals. By measuring the motion of a body against a ruler, the average velocity of the particle between points can be found and hence the acceleration.

Ticker Timer – Operates on the same principle as a strobe light. A pen is made to strike a piece of tape so many times per second (typically 50). By measuring the distance between each mark on the tape, the average velocity of the particle between marks can be found and hence the acceleration. Typically the distance between more than one mark is taken. To check the acceleration is constant, the distance travelled between a certain number of marks can be plotted as below as time progresses. If a line drawn throw the midpoint of the bar peaks makes a straight line, then the acceleration is constant.

For example 5 ticks in the diagram above are made in the first 2 cm of tape and 5 in the last 10 cm (note the first tick only marks the start).

Henceand

The time between the first and second strips is taken asThis is the time from the middle of the first strip to the middle of the second.

The acceleration is