Question

The $x$ coordinates of a particle at any time $t$ are given by $x=7t+4t^2$ where $x$ is in $m$ and $t$ in $\text{s}$. The acceleration of the particle at $5\text{s}$ is

• A. zero
• B. $8{\text{m/s}}^2$
• C. $20{\text{m/s}}^2$
• D. $40{\text{m/s}}^2$

Answer 1

The correct option is B $8{\text{m/s}}^2$

To get acceleration along $x-$axis we need to differentiate $x\left(t\right)$ twice
$x\left(t\right)=7t+4t^2$
$\Rightarrow a_x=\frac{d^{2}x}{d{t}^2}=8{\text{m/s}}^2$