Question

A particle is travelling along a straight line $OX$ . The distance $x$ of the particle from $O$ at a time $t$ is given by $x=37+27t–t^3$, where $t$ is time in $second$. The distance of the particle from $O$ when it comes to rest is

• A. $81m$
• B. $91m$
• C. $101m$
• D. $111m$

Answer 1

The correct option is B

$91m$

Step 1: Given data

Distance, $x=37+27t–t^3$

Step 2: Find time

Velocity, $v$ is the rate of change of the distance, $x$ with respect to the time, $t$

$$\begin{gathered} v=\frac{dx}{dt} \\ v=\frac{d}{dx}\left(37+27t-t^3\right) \\ v=27–3t^2 \end{gathered}$$

When

$$\begin{gathered} v=0, \\ 27–3t^2=0 \\ t=3s \end{gathered}$$

Step 3. Find the distance, $x$

Putting the value of the time in given equation of the distance, we get

$$\begin{gathered} x=37+27\left(3\right)–{\left(3\right)}^3 \\ x=91m \end{gathered}$$

Hence, option $\left(B\right)$ is correct.