   Next: Free-fall under gravity Up: Motion in 1 dimension Previous: Motion with constant velocity

## Motion with constant acceleration

Motion with constant acceleration occurs in everyday life whenever an object is dropped: the object moves downward with the constant acceleration , under the influence of gravity.

Fig. 8 shows the graphs of displacement versus time and velocity versus time for a body moving with constant acceleration. It can be seen that the displacement-time graph consists of a curved-line whose gradient (slope) is increasing in time. This line can be represented algebraically as (19)

Here, is the displacement at time : this quantity can be determined from the graph as the intercept of the curved-line with the -axis. Likewise, is the body's instantaneous velocity at time . The velocity-time graph consists of a straight-line which can be represented algebraically as (20)

The quantity is determined from the graph as the intercept of the straight-line with the -axis. The quantity is the constant acceleration: this can be determined graphically as the gradient of the straight-line (i.e., the ratio , as shown). Note that , as expected.

Equations (19) and (20) can be rearranged to give the following set of three useful formulae which characterize motion with constant acceleration:   (21)   (22)   (23)

Here, is the net distance traveled after seconds.

Fig. 9 shows a displacement versus time graph for a slightly more complicated case of accelerated motion. The body in question accelerates to the right [since the gradient (slope) of the graph is increasing in time] between times and . The body then moves to the right (since is increasing in time) with a constant velocity (since the graph is a straight line) between times and . Finally, the body decelerates [since the gradient (slope) of the graph is decreasing in time] between times and .    Next: Free-fall under gravity Up: Motion in 1 dimension Previous: Motion with constant velocity
Richard Fitzpatrick 2006-02-02