Answer:
Consider the velocity-time
graph of an object that moves under uniform acceleration as shown in the figure
. From this graph, we can see
that initial velocity of the object (at point A) is u and then it increases to
v (at point B) in time t. The velocity changes at a uniform rate a.
As shown in the figure, the lines BC and BE are drawn from point B on the time
and the velocity axes respectively, so that the initial velocity is represented
by OA, the final velocity is represented by BC and the time interval t is
represented by OC. BD = BC - CD, represents the change in velocity in time
interval t.
If we draw AD parallel to OC, we observe
that BC = BD + DC = BD + OA
Substituting, EC with v and OA with u, we
get
V=BD + u
Or BD = v ? u
?? (1)
Thus from the given velocity-time graph,
the acceleration of the object is given by
Substiuting, OC with t, we get
or BD =
at ?..(2)
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