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
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 = ........................... (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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