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CBSE Class 9 Answered

Show that the area under velocity time graph for uniformly increasing velocity is equal to the distance covered by the body
Asked by snehanath217 | 09 Apr, 2023, 07:56: PM
answered-by-expert Expert Answer
Let the initial velocity of object be u . Let v be the velocity after time duration t.
If change in velocity with respect to time is uniform, then average velocity uavg in this time duration is
 
begin mathsize 14px style u subscript a v g end subscript space equals space fraction numerator u plus v over denominator 2 end fraction end style
 
Distance S travelled is
 
S  = uavg × t = (1/2) ( u + v ) t  . . . . . . . . . . . . . . . . . . .  . (1)
 
Graph below shows the typical variation of velocity that increases uniformly ( constant acceleration )
 
Line AB shows that velocity varies uniformly from u to v in time t . Time duration is shown as CD on time axis.
 
If we compare the expression given in eqn.(1) and area under the graph line AB , we see that area under the graph line AB is a trapezium as given by eqn.(1)
 
Hence , when velocity changes uniformly, then area under the velocity-time graph is the diplacement made in given time
 

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