Question

The distance moved by a particle travelling in a straight line in $t$ seconds is given by $s=45t+11t^2-t^3$. The time taken by the particle to come to rest is

• A. $\frac{5}{3}$ sec
• B. $0$ sec
• C. $9$ sec
• D. $\frac{3}{5}$ sec

Answer 1

The correct option is C $9$ sec

Speed = $\frac{d}{dt}$(distance)

$s=45t+11t^2-t^3$

$v=45+22t-6t^2$

When particle comes to rest $v=0$

Solving the quadratic equation, we get

$t=\frac{-22\pm \sqrt{{22}^2+4\times 45\times -6}}{2\times -6}$

$t=-\frac{5}{3}$ or $9$

Hence time taken is $9$ seconds