A stone thrown vertically upward satisfies the equation `s= 64 t -16t^(2)` where is in meter and t is second .What is the time required to reach the maximum height ?

Options

A. 1s
B. 2s
C. 3s
D. 4s

Answer

B

Explanation

Give equation is `S =64 t -16 t^(2)`
`therefore` on differentaiating w.r.t we get
`(ds)/(dt)=64-32t `
Put `(ds)/(dt)=0` for maximum height
`rarr 64 -32 t =0 rarr t=2`
Now `(d^(2)s)/(dt^(2))=-32`
At `t=2 , (d^(2)s)/(dt^(2))=-32`
`therefore` Required time =2 second