Question

The velocity-displacement graph of a particle is shown in Fig . (a) Write the relation between (v) and (x).
(b) Obtain the relation between acceleration and displacement and plot it .
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Answer 1

Given, initial velocity `= v_(0)`
Let the distance travelled in time `t = x_(0)`
For the graph `tan theta = (v_(0))/(x_(0)) = (v_(0) - v)/(x)`
where, v is velocity and x is displacement at any instant of time t.
From eq. (i)
`v_(0) - v = (v_(0))/(x_(0))x`
`rArr v = (-v_(0))/(x_(0)) = x + v_(0)`
We know that
Acceleration `a = (dv)/(dt) = (-v_(0))/(x_(0)) (dx)/(dt) +0`
`rArr a = (-v_(0))/(x_(0)) (v)`
`= (-v_(0))/(x_(0)) ((-v)/(x_(0)) x + v_(0))`
`= (v_(0^(2)))/(x_(0^(2))) x - (v_(0^(2)))/(x_(0))`
Graph of a versus x is given above.