Question

A particle is moving along the $x-$axis whose acceleration is given by $a=3x-4$, where $x$ is the location of the particle. At $t=0$, the particle is at rest at $x=4/3m$. The distance travelled by the particle in $5s$ is

• A. Zero
• B. $42m$
• C. Infinite
• D. None of these

Answer 1

The correct option is A Zero

$t=0$,
$x=\frac{4}{3}$ and
$V=0$
$=0=3\times {\left(\frac{4}{3}\right)}^2-8\times \frac{4}{3}+C$
$C=\frac{32}{3}-\frac{16}{3}=\frac{16}{3}$
$v=\sqrt{3x^2-8x+\frac{16}{3}}$$
Now see
at $x=\frac{4}{3}$
$a=3x-4$
$=3\times \frac{4}{3}-4$
$=a=0$
it will no move angular
$S=0$