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 ?

Options

A.
B.
C.
D.

Answer

A

Explanation

Given line has positive intercet but negative slopr. So its equation can be written as
`upsilon=-mx+upsilon_(0)["where ", m=tan theta=(upsilon_(0))/(x_(0))]` ….(i)
By differentiating with respect to time, we get
`(d upsilon)/(dt)=-m(dx)/(dt)=-m upsilon`
Now substituting the value of `upsilon` from Eq. (i), we get
`(d upsilon)/(dt)=-m[-mx+upsilon_(0)]=m^(2)x-m upsilon_(0)`
`therefore a=m^(2)x-m upsilon_(0)`
i.e., the graph between a and x should have positive slope but negsative intercept on a-axis. So, graph (a) is correct.