Question

The displacement $x$ of a body varies with time as $x=-\frac{1}{3}{{t}^{2}}+16t+3$ where $x$ is in metre and t in second. The time taken by the body to come to rest is

• A. 12s
• B. 24s
• C. 30s
• D. 36s

Answer 1

Answer: (B)

24s

Answer 2

$x=-\frac{1}{3}{{t}^{2}}+16t+3$ Velocity, $v=\frac{dx}{dt}$ $=\frac{d}{dt}\left( -\frac{1}{3}{{t}^{2}}+16t+3 \right)$ $=-\frac{2}{3}t+16$ The body comes to rest, so $v=0$ i.e., $-\frac{2}{3}t+16=0$ $\Rightarrow$ $\frac{2}{3}t=16$ $t=\frac{16\times 3}{2}$ $=24\,s$