Question

A particle moves in a line with velocity given by $\frac{ds}{dt}=s+1$. The time taken by the particle to cover a distance of $9$ meter is

• A. $1$
• B. $\log 10$
• C. $2\log ,10$
• D. $10$

Answer 1

The correct option is B $\log 10$

Velocity of particle $=v=s+1$

$\therefore \frac{ds}{dt}=(s+1)$

$\therefore \frac{ds}{s+1}=dt$

Integrating both sides, we have

${\int }_0^s\frac{ds}{s+1}={\int }_0^{t}dt$

$\therefore \ln (s+1)-\ln (0+1)=t-0$

$\therefore t=\ln (s+1)$

$\therefore t=\ln 10={\log }_{e}10$ (for $s=10$)

$\therefore t=2.3$ seconds