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)

Displacement of a body,
$x = - \frac{1}{3} t^2 + 16 t + 3 \,\,[\because v = \frac{dx}{dt}]$
From the question, $v = 0$
$\frac{d x}{d t}=0$
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 $24 \,s$.