A particle is moving in a straight line according to graph given below : (a is acceleration, `v` is velocity, `x` is position, `t` is time) :

Options

A.
B.
C.
D.

Answer

A, B, D

Explanation

Given `v = x` & `t = 0`
`a = (dv)/(dt) = (dx)/(dt)` & `v,.(dv)/(dx) = x`
`rArr a = v = x overset(v)underset(l)(int)v.dv = overset(v)underset(l)(int)x.dx`
`v(2)/(1)'^(v) = x(2)/(1)'^(v) rArr v = x`
`(dx)/(dt) = x`
`overset(v)underset(l)(int)(dx)/(x) = overset(v)underset(0)(int)dt_(2) rArr lnx = t`
`x = e^(1)`