Question

Find the acceleration of the particle at $x=3\text{m}$.

• A. $36{\text{m/s}}^2$
• B. $-48{\text{m/s}}^2$
• C. $-36{\text{m/s}}^2$
• D. $48{\text{m/s}}^2$

Answer 1

The correct option is D $48{\text{m/s}}^2$

As we know that
acceleration, $a=v\frac{dv}{dx}$
So, we can write the equation for $v$ as a function of $x$ from the given curve as
$v=mx+c$
where, $c=0$ and $m=\frac{dv}{dx}=\frac{-20-0}{5}=-4$
Thus, $v=-4x\Rightarrow v{|}_{@x=3\text{m}}=-4\times 3=-12\text{m/s}$
Hence, acceleration will be
$a=v\cdot m=-12\times -4=48{\text{m/s}}^2$