Galileo reasoned that the velocity of a ball rolling down a slope should increase at a uniform rate. That is, its motion should be uniformly accelerated. The velocity v of a uniformly accelerated body which has travelled through a distance d can be shown to satisfy the equation of motion

where u is initial velocity and a is acceleration. The purpose of this experiment is to test the validity of this equation and use it to determine the rate of acceleration for a ball rolling down a slope.

Incline the ramp at an angle great enough to allow the ball to accelerate swiftly down it. Set the light probe at a measured distance down the track as in the diagram. Let the ball run down the track past the probe. Use the logged data to determine the time interval that the ball is passing the probe. Determine the distance the ball travels while it is blocking the probe and use the measurements to calculate the velocity of the ball as it passes the light probe at the end of the track.

Repeat the experiment measuring the velocity when the ball is released at different distances down the ramp. Think carefully about where you should measure the distances from.

Plot the data obtained on a graph of v² vs d so that the above equation relating velocity and distance can be confirmed. Use this graph to determine the acceleration of the rolling ball.

Design an extension of the above procedure to investigate how the acceleration of the ball depends on the height of the ramp.