Question

A particle, initially at origin moves along $x$ axis according to the rule $\frac{dx}{dt}=x+4$. The time taken by the particle to traverse a distance of $96$ units is

• A. $3\ln 5$
• B. $\ln 5$
• C. $2\ln 5$
• D. None of these

Answer 1

Answer: (D)

None of these

Given $\frac{dx}{dt}=x+4$

$\Rightarrow \frac{dx}{x+4}=dt$

By applying integration on both sides , we get $\ln (x+4)=t+k$

$\Rightarrow x=e^t-4+C$

At $t=0$ , $x=0$ , which implies $C=3$

Therefore the equation becomes $x=e^t-1$

Given that $x=96$ , which implies $t=\ln 97$