Introduction to Acceleration
Acceleration is the rate of change of velocity with time. The average acceleration, a, is given by:
The usual units are metres per second squared (m/s2 or m sð2 ). If u is the initial velocity of an object in metres per second, v is the final velocity in metres per second and t is the time in seconds elapsing between the velocities of u and v, then:
A graph of velocity (scale on the vertical axis) against time (scale on the horizontal axis) is called a velocity/time graph, as introduced in Chapter 7. For the velocity/time graph shown in Figure 8.1, the slope of line OA is given by (AX/OX). AX is the change in velocity from an initial velocity, u, of zero to a final velocity, v, of 4 metres per second. OX is the time taken for this
change in velocity, thus
In general, the slope of a line on a velocity/time graph gives the acceleration. The words ‘velocity’ and ‘speed’ are commonly interchanged in everyday language. Acceleration is a vector quantity and is correctly defined as the rate of change of velocity with respect to time. However, acceleration is also the rate of change of speed with respect to time in a certain specified direction.
Free-fall and Equation of Motion
If a dense object such as a stone is dropped from a height, called free-fall, it has a constant acceleration of approximately 9.8 m/s2. In a vacuum, all objects have this same constant acceleration, vertically downwards, that is, a feather has the same acceleration as a stone. However, if free-fall takes place in air, dense objects have the constant acceleration of 9.8 m/s2 over short distances, but objects that have a low density, such as feathers, have little or no acceleration.
For bodies moving with a constant acceleration, the average acceleration is the constant value of the acceleration, and since from earlier:
For example, if a stone is dropped from an aeroplane the stone is free falling and thus has an acceleration, a, of approximately 9.8 m/s2 (taking downward motion as positive). The initial downward velocity of the stone, u, is zero. The velocity v after 2s is given by: v D u C at D 0 C 9.8 ð 2 D 19.6 m/s, i.e. the velocity of the stone after 2 s is approximately 19.6 m/s.