Search any question & find its solution
Question:
Answered & Verified by Expert
If the distance ' $S$ metres traversed by a particle in $t$ seconds is given by $S=t^{3}-3 t^{2}$, then the velocity of the particle when the acceleration is zero, in $\mathrm{m} / \mathrm{sec}$ is
Options:
Solution:
2906 Upvotes
Verified Answer
The correct answer is:
$-3$
We have,
$$
\begin{aligned}
&S=t^{3}-3 t^{2} \\
&\Rightarrow \frac{d S}{d t}=3 t^{2}-6 t \text { and } \frac{d^{2} S}{d t^{2}}=6 t-6 \\
&\text { Now, acceleration, } \frac{d^{2} S}{d t^{2}}=0 \\
&\Rightarrow 6 t-6=0 \\
&\Rightarrow \quad t=1 \\
&\therefore \text { Velocity }=\left.\frac{d S}{d t}\right|_{t=1} \\
&\quad=3(1)^{2}-6(1)=3-6=-3 \mathrm{~m} / \mathrm{sec}
\end{aligned}
$$
$$
\begin{aligned}
&S=t^{3}-3 t^{2} \\
&\Rightarrow \frac{d S}{d t}=3 t^{2}-6 t \text { and } \frac{d^{2} S}{d t^{2}}=6 t-6 \\
&\text { Now, acceleration, } \frac{d^{2} S}{d t^{2}}=0 \\
&\Rightarrow 6 t-6=0 \\
&\Rightarrow \quad t=1 \\
&\therefore \text { Velocity }=\left.\frac{d S}{d t}\right|_{t=1} \\
&\quad=3(1)^{2}-6(1)=3-6=-3 \mathrm{~m} / \mathrm{sec}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.