Question

Suppose the initial position of the particle is $s\left(0\right)=9$, then what will be the particle's position at $t=1$ sec?

• A. $\frac{8}{3}$
• B. $\frac{16}{3}$
• C. $\frac{4}{3}$
• D. $\frac{11}{3}$

Answer 1

The correct option is B $\frac{16}{3}$

Given $\frac{ds}{dt}=V\left(t\right)=t^2-\frac{8}{{(t+1)}^2}$

$\Rightarrow S=\int t^2-\frac{8}{{(t+1)}^2}=\frac{t^2}{3}+\frac{8}{(t+1)}$

$\Rightarrow S_{@t=1}=\frac{1}{3}+\frac{8}{2}=\frac{1}{3}+4$

$=\frac{16}{3}$

Hence, the answer is $\frac{16}{3}.$