First slide
Instantaneous acceleration
Question

The given graph shows the variation of velocity with displacement. Which one of the graphs given below correctly represents the variation of acceleration with displacement?

Moderate
Solution

Given line has positive intercept but negative slope. So, its equation can be written as

               v=-mx+v0 where, m=tanθ=v0x0                         …(i)

By differentiating with respect to time, we get

             dvdt=-mdxdt=-mv

Now, substituting the value of v from Eq. (i), we get

              dvdt=-m-mx+v0=m2x-mv0

              a = m2x - mv0

i.e. The graph between a and x should have positive slope but negative intercept on a-axis. So, graph (1) is correct.

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