Question

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

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

Answer 1

Answer: (B)

$24\,s$

Answer 2

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