the displacement of particle is given by `X= a_(0) + (a_(1)t)/(2)-(a_(2)t^(2))/(3)` . What is its acceleration?

Options

A. `(2a_(2))/(3)`
B. `-(2a_(2))/(3)`
C. `a_(2)`
D. zero

Answer

B

Explanation

Displacement `X = (a_(0)+a_(1)t)/(2) - (a_(2)t^(2))/(3)`
Velocity `v = (dx)/(dt)`
`= (d)/(dt) (a_(0) +(a_(1)t)/(2)-(a_(2)t^(2))/(3))`
`v = (a_(1))/(2)- (2a_(2)t)/(3)`
Acceleration `a = (dv)/(dt) = (d)/(dt) ((a_(1))/(2) - (2a_(2)t)/(3))`
`= (-2a_(2))/(3)`