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

The Correct Option is B

$ 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 $