## 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. 1 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

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 .

*straight-line*which can be represented algebraically as

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 (1) and (2) can be rearranged to give the following set of three useful formulae which characterize motion with constant acceleration:

Here, is the net distance traveled after seconds. Fig. 2 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 .

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