The velocity `(upsilon)` of a particle moving along X-axis varies with its position x as shown in figure. The acceleration (a) of particle varies with position (x) as

Options

A. `a^(2)=x+3`
B. `a=2x^(2)+4`
C. `2a=3x+5`
D. `a=4x-8`

Answer

D

Explanation

Given velocity `(upsilon)`- position (x) graph is shown in figure.

We know that acceleration `a=(upsilon d upsilon)/(dx)` …(i)
From the graph, we have
`(x)/(2)+(upsilon)/(4)=1 rArr 2x+upsilon=4` ....(ii)
`rArr (d upsilon)/(dx)=-2` ....(iii)
From Eqs. (i), (ii) and (iii)
`a=(4-2x)(-2)=-8+4x rArr a=4x-8`