Question

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

• A. $12s$
• B. $24s$
• C. $30s$
• D. $36s$

Answer 1

Answer: (B)

Displacement of a body,
$x=-\frac{1}{3}{t}^2+16t+3[\because v=\frac{dx}{dt}]$
From the question, $v=0$
$\frac{dx}{dt}=0$
or $\frac{d}{dt}(-\frac{1}{3}{t}^2+16t+3)=0$
or $-\frac{2}{3}t+16+0=0$
or $-\frac{2}{3}t=-16$
or $t=\frac{16\times 3}{2}=24s$
So, time taken by the body to come to rest is $24s$.