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CBSE Class 11-science Answered

can we check using dimensional analysis that the area under the v-t graph gives us the displacment and the slope of the v-t graph gives us the accerleration .  i am not understanding the 
Asked by Suresh | 02 Jul, 2019, 08:18: PM
answered-by-expert Expert Answer
Figure shows the velocity-time graph between time t1 and t2 .  Let us consider a small time interval Δt and v be the velocity during this time interval.
 
Then area under the curve in this time interval = v×Δt 
 
Area under the curve during different time interval between t1 and t2 is given by,      Area = begin mathsize 14px style sum from i equals 0 to n of v subscript i cross times increment t end style  ........................... (1)
where vi are magnitude of velocities at different time interval. 
 
If we do dimensional analysis for RHS of eqn.(1), then dimension of   v×Δt  =  ( L / T ) (T)  = (L)
 
Hence Area under v-t curve has dimension of length. Hence Area under the v-t curve gives displacement.
 
figure shows the slope of v-t graph,   slope = Δv / Δt  ........................(2)
 
Dimensional analysis of RHS of eqn.(2) gives,  dimension of slope = ( L/T ) / T  = L/T2 ..............(3)
 
i.e., dimension of slope of v-t graph is same as that of acceleration.
 
Hence slope of v-t graph gives acceleration.
Answered by Thiyagarajan K | 02 Jul, 2019, 09:00: PM
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