The displacement (x) of a particle depends on time t as `x=alpha t^(2)-beta t^(3)`. Choose the incorrect statements from the following.

Options

A. The particle will return to its starting point after time `alpha //beta `
B. The particle will come to rest after time ` 2alpha//3beta `
C. The initial velocity of the particle was zero but its initial acceleration was not zero
D. No net forced will act on the particle at `t= alpha//3beta`

Answer

A, B, C, D

Explanation

` x(t) =alpha t^(2) -beta t^(3) , " " v(t) =2alpha t-3beta t^(2) ," " a(t) =2alpha - 6 beta t `
(A) ` Delta x= x (t) -x(0) rArr alpha t^(2) -beta t^(3) =0 " "rArr " " t=alpha //beta `
(B) ` v(t) =0 " "rArr " " t =2alpha //3 beta `
(C) ` v(0) =0 and a(0) -2alpha -6 beta (0) =2alpha ne 0`
(D) ` a(t) =0 " "rArr " "2alpha -6beta t =0 " "rarr " "t= alpha //3 beta `
So , at t `= alpha//3 beta, ` acceleration of the particle is zero, so no net force acts on it.