A particle moves along a straight line OX . At a time t (in seconds) distance x (in metres ) of part

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2.Motion in Straight Line

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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 ?..........$m$

$16$

$24$

$40$

$56$

(AIPMT-2006)

Solution

$\begin{array}{l}
x = 40 + 12t – {t^3}\\
\therefore \,\,Velocity\,V = \frac{{dx}}{{dt}} = 12 – 3{t^2}\\
When\,particle\,come\,to\,rest,\,dx/dt = v = 0\\
\therefore \,12 – 3{t^2} = \, \Rightarrow \,3{t^2} = 12\, \Rightarrow \,t = 2\,\,\sec .\\
{\rm{Distance}}\,travelled\,by\,the\,particle\,before\,
\end{array}$

$\begin{array}{l}
{\rm{coming}}\,to\,rest\\
\int\limits_0^s {ds = } \int\limits_0^2 {vdt} \,\,\,\,s = \int\limits_0^2 {\left( {12 – 3{t^2}} \right)dt = 12t – } \left. {\frac{{3{t^3}}}{3}} \right|_0^2\\
s = 12 \times 2 – 8 = 24 – 8 = 16\,m.
\end{array}$

Standard 11

Physics

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medium

(NEET-2016)

we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why ?

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The figure shows a velocity-time graph of a particle moving along a straight line If the particle starts from the position $x_0=-15\,m$ , then its position at $t=2\,s$ will be …….. $m$

medium

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 ?..........$m$

Solution

Similar Questions

Two cars $P$ and $Q$ start from a point at the same time in a straight line and their positions are represented by $ x_p(t)=at+bt^2 $ and $x_Q(t)= ft- t^2$. At what time do the cars have the same velocity $?$

we have carefully distinguished between average speed and magnitude of average velocity. No such distinction is necessary when we consider instantaneous speed and magnitude of velocity. The instantaneous speed is always equal to the magnitude of instantaneous velocity. Why ?

For the displacement-time graph shown in figure, the ratio of the magnitudes of the (constant) speeds during the first two seconds and the next four seconds is

What does the area of $v\to t$ graph of moving object represent ?

The figure shows a velocity-time graph of a particle moving along a straight line If the particle starts from the position $x_0=-15\,m$ , then its position at $t=2\,s$ will be …….. $m$

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