Derive the distance-time equation by graphical method.
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Equations of motion by graphical method
We already know about equations of motion when an object moves along straight line with uniform acceleration. We already know how to derive them but these equations can also be derived by graphical method.
a. Equation for velocity time relation
Consider the velocity-time graph of an object that moves under uniform acceleration as shown below in the figure 7.
From this graph, you can see that initial velocity of the object is
u
(at point A) and then it increases to
v
(at point B) in time
t
. The velocity changes at a uniform rate
a
.
Again from figure it is clear that time
t
is represented by OC , initial velocity
u
by OA and final velocity of object after time
t
by BC.
v-t graph to derive equations of motion
From graph as given in figure 7 it is clear that
B
C
=
B
D
+
D
C
=
B
D
+
O
A
.
So we have
v=BD+u (1)
We should now find out the value of BD. From the velocity-time graph (Fig. 7), the acceleration of the object is given by
which gives,
B
D
=
a
t
putting this value of BD in equation 1 we get
v
=
u
+
a
t
which is the equation for velocity time relation.