Question

Find the total distance traveled by the particle.

• A. $24.95$
• B. $42.59$
• C. $56.56$
• D. $49.49$

Answer 1

The correct option is B $42.59$

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

$\Rightarrow S={\int }_0^5{t}^2-\frac{8}{{(t+1)}^2}dt$

$={[\frac{t^2}{3}+\frac{8}{(t+1)}]}_0^5$

$=\frac{125}{3}+\frac{8}{6}=\frac{125+4}{3}$

$=43.$

Hence, the answer is $\mathrm{42.59.}$