Search any question & find its solution
Question:
Answered & Verified by Expert
A block of mass $1 \mathrm{kg}$ starts from rest at $x=0$ and moves along the $X$ -axis under the action of a force $F=k t,$ where $t$ is time and
$k=1 \mathrm{Ns}^{-1}$. The distance the block will trave] in 6 seconds is
Options:
$k=1 \mathrm{Ns}^{-1}$. The distance the block will trave] in 6 seconds is
Solution:
1773 Upvotes
Verified Answer
The correct answer is:
$36 \mathrm{m}$
From Newton's second law
$$
\begin{array}{l}
F=m a \\
m=1 \mathrm{kg} \\
F=1 \times a=\frac{d v}{d t}
\end{array}
$$
According to the question,
$$
F=k t=\frac{d v}{d t}
$$
$$
d v=k t \cdot d t
$$
Integration gives
$$
\begin{aligned}
v &=\frac{k t^{2}}{2}=\frac{d x}{d t} \\
x &=\frac{k t^{3}}{6}=\frac{1 \times 6 \times 6 \times 6}{6} \\
&=36 \mathrm{m}
\end{aligned}
$$
$$
\begin{array}{l}
F=m a \\
m=1 \mathrm{kg} \\
F=1 \times a=\frac{d v}{d t}
\end{array}
$$
According to the question,
$$
F=k t=\frac{d v}{d t}
$$
$$
d v=k t \cdot d t
$$
Integration gives
$$
\begin{aligned}
v &=\frac{k t^{2}}{2}=\frac{d x}{d t} \\
x &=\frac{k t^{3}}{6}=\frac{1 \times 6 \times 6 \times 6}{6} \\
&=36 \mathrm{m}
\end{aligned}
$$
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.