Question

A stone thrown vertically upwards satisfies the equations $s=8t-16t^2$. The time required to reach the maximum height is.

• A. $2s$
• B. $4s$
• C. $0.25s$
• D. $2.5s$

Answer 1

The correct option is C $0.25s$

$S=8t-{16t}^2$

diff. both sides w.r.t. $t$

$\frac{ds}{dt}=8-32t$

To maximize height but $\frac{ds}{dt}=0$

$\therefore$ $8-32t=0$

$t=\frac{8}{32}=\frac{1}{4}$

$\frac{d^{2}s}{{dt}^2}=\frac{d}{dt}[8-32t]$

$=-32<0$

$\therefore$ At $t=\frac{1}{4},S$ maximum

$t=0.25s$