CBSE Class 11-science Answered
Show that area under the v-t graph of an object in uniform motion gives the displacement of the object in a given time.
Asked by Topperlearning User | 17 Apr, 2014, 12:55: PM
Expert Answer
Let us consider an object moving with uniform velocity
.
Also, displacement of the object in the time interval between t and t' is given by
Since the object is in uniform motion, therefore the velocity will always be v and the velocity time graph will be along a straight line parallel to time axis.
Let A and B are two point on the v-t graph corresponding to instants t and t'.
Therefore, AA'= BB'= v
Also, A'B'=AB= t'-t
Area under v-t graph between t and t'=area ABB'A'=AA' x A'B' = v (t'-t) (ii)
But according to equation (i) we have
therefore, x' -x = area ABB'A'
that is area under the v-t graph of an object in uniform motion gives the displacement of the object in a given time.
Answered by | 17 Apr, 2014, 02:55: PM
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