The displacement of a particle is `s = (a+bt)^(6)`, where a and b are constants. Find acceleration of the particle as a function of time.

Options

A. `30b^(2)(a+bt)^(4)`
B. `30b^(2)(a+bt)^(3)`
C. `6b^(2)(a+bt)^(5)`
D. `30b^(2)(a+bt)^(5)`

Answer

C

Explanation

Let F be the force of air resistance. For the upward motion Facts downward. Let `a_(1)` = retardation (downward acceleration).
`mg+F=ma_(1) " or "a_(1) = g +(F)/(m)` Thus `a_(1) gt a_(2)`
Let h = maximum height reached
`h=(1)/(2)a_(1)t_(1)^(2)=(1)/(2)a_(2)t_(1)^(2)`