The displacement of a particle along x-axis is given by x = 3 +`8t-2t^(2)` . What is its acceleration? At what time it will come into rest ? All are in SI units.

Explanation

Displacement x = `3 +8t-2t^(2)`,
velocity v = `(dx)/(dt)` = 8-4 t,
acceleration a = `(dv)/(dt) = -4 "m.s"^(-2)`.
The negative value means that the particle is moving with a uniform retardation .
When the particle comes to rest,
v= 0 , i.e, 8-4t = 0
`:.` t = 2 s