The displacement (in metre) of a particle varies with time (in second) according to the equation `y =- (2)/(3) t ^(2) + 16 t +2.` How long does the particle take to come to rest ?

Options

A. 12 s
B. 8 s
C. 16 s
D. 10 s

Answer

A

Explanation

The displacement of a particle
`y =- 2/3 t ^(2) + 16 t +2`
`therefore` Velocity `u = (dy)/(dt) = (d)/(dt) [- (2)/(3) t ^(2) + 16 t +2]`
`therefore v = -(4)/(3) t + 16`
When a particle is at rest, v =0
`therefore 0=- (4)/(3) t + 16`
`therefore 4/3 t = 16`
`therefore t = 12s.`