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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 displacementtime graph consists of
a curvedline 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
curvedline with the axis. Likewise, is the body's instantaneous
velocity at time .
Figure 8:
Graphs of displacement versus time and velocity versus time
for a body moving with constant acceleration

The velocitytime graph consists of a straightline which can be represented
algebraically as

(20) 
The quantity is determined from the graph as the intercept of the
straightline with the axis. The quantity is the constant acceleration: this
can be determined graphically as the gradient of the straightline
(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:
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 .
Figure 9:
Graph of displacement versus time

Next: Freefall under gravity
Up: Motion in 1 dimension
Previous: Motion with constant velocity
Richard Fitzpatrick
20060202