Question

The motion of a particle along a straight line is
described by equation x = 8 + 12t - p, where x is
in metre and t in second. The retardation of the
particle when its velocity becomes zero is
[AIPMT (Prelims)-2012]

in the ans how do they integrate acceleration​

Answer 1

Correct Question:-

The motion of a particle along a straight line is  described by the equation $\sf{x=8+12t-t^3,}$ where $\sf{x}$ is  in metre and $\sf{t}$ in second. Find the retardation of the  particle when its velocity becomes zero.

Solution:-

The velocity of the particle is,

$\longrightarrow\sf{v=\dfrac{dx}{dt}}$

$\longrightarrow\sf{v=\dfrac{d}{dt}\,\left[8+12t-t^3\right]}$

$\longrightarrow\sf{v=12-3t^2}$

We have to find the retardation of the particle at the time when the velocity becomes zero.

$\longrightarrow\sf{v=0}$

$\longrightarrow\sf{12-3t^2=0}$

$\longrightarrow\sf{3t^2=12}$

$\longrightarrow\sf{t^2=4}$

Since $\sf{t\geq0,}$

$\longrightarrow\sf{t=2}$

The retardation of the particle is,

$\longrightarrow\sf{a=\dfrac{dv}{dt}}$

$\longrightarrow\sf{a=\dfrac{d}{dt}\,\left[12-3t^2\right]}$

$\longrightarrow\sf{a=-6t}$

At $\sf{t=2,}$

$\longrightarrow\sf{a=-6\times2\ m\,s^{-2}}$

$\longrightarrow\sf{\underline{\underline{a=-12\ m\,s^{-2}}}}$

Answer 2

Answer:

Hello mate ✌️

Explanation:

The motion of a particle along a straight line is described by equation

The motion of a particle along a straight line is described by equation : `x = 8 + 12 t - t^3` where `x` is in metre and `t` in second. The retardation of the particle when its velocity becomes zero is

hope it will be helpful to you ✌️

itz Essar 03 ❤️