Question

Find the acceleration of the particle at $x=2\text{m}$.

• A. $-30.5{\text{m/s}}^2$
• B. $-37.5{\text{m/s}}^2$
• C. $37.5{\text{m/s}}^2$
• D. $30.5{\text{m/s}}^2$

Answer 1

The correct option is B $-37.5{\text{m/s}}^2$

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, $c=20$ and $m=\frac{dv}{dx}=\frac{10-20}{4-0}=-2.5$
Thus, $v=-2.5x+20\Rightarrow v{|}_{@x=2\text{m}}=-2.5\times 2+20=15\text{m/s}$
Hence, acceleration will be
$a=v\cdot m=15\times -2.5=-37.5{\text{m/s}}^2$