Question

A particle moves along a straight line $OX$. At a time $t$ (in seconds) the distance $x$ (in metres) of the particle from $O$ is given by $x=40+12t-t^3$. How long would the particle travel before coming to rest?

• A. $24m$
• B. $40m$
• C. $56m$
• D. $16m$

Answer 1

The correct option is D $16m$

Distance/time is speed so just differentiate the x $w.r.t$ time we get soeed $v=0+12-3t^2$

Now to come at rest the speed should be zero so now equating the $v=0$ we get $t=2seconds$.

The value of x at $t=0$ is $40m$ and the value of x at $t=2second$ is $56m$ so distance trevelled in $2$ seond will be $56-40=16m$

Option D is correct.