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, 20:18: PM
![](https://images.topperlearning.com/topper/tinymce/imagemanager/files/2cade5f352fd85fc1908a28659ac0a445d1b74c48d3a07.93895760vtgraph.png)
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)
![begin mathsize 14px style sum from i equals 0 to n of v subscript i cross times increment t end style](https://images.topperlearning.com/topper/tinymce/cache/af4c39bb1bedf82c8fef8bf7ef2a3952.png)
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, 21:00: PM
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