The displacement x of a particle depend on ti | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Given, $x=\alpha t^2-\beta t^3$
Particle will return to its starting point when, $x =\alpha t ^2-\beta t ^3=0$
or,
$t=\frac{\alpha}{\beta}$
Veloci

Vedclass · Accepted Answer

All of the above

Vedclass · Answer

Given, $x=\alpha t^2-\beta t^3$
Particle will return to its starting point when, $x =\alpha t ^2-\beta t ^3=0$
or,
$t=\frac{\alpha}{\beta}$
Velocity $= v =\frac{ dx }{ dt }=2 t \alpha-3 \beta t ^2 \ldots \ldots (1)$
at $t =0, v =0$ so the initial velocity zero.
Acceleration $= a =\frac{ dv }{ dt }=2 \alpha-6 t \beta \ldots \ldots(2)$
at $t =0, a =2 \alpha$ so initial acceleration does not zero.
The particle will come to rest when, 2 t $\alpha-3 \beta t ^2=0$ from $(1)$
or, $t=\frac{2 \alpha}{3 \beta}$
$At , t =\frac{\alpha}{3 \beta}, a =2 \alpha-6 \beta\left(\frac{\alpha}{3 \beta}\right)=0$
so net force $= ma =0$, thus no net force act on the particle when $t =\frac{\alpha}{3 \beta}$

The displacement $x$ of a particle depend on time $t$ as $x = \alpha {t^{^2}} - \beta {t^3}$

Similar Questions

Write equations of motion for uniformly acceletated motion in plane ?

Consider a point $P$ on the circumference of a disc rolling along a horizontal surface. If $R$ is the radius of the disc, the distance through which $P$ moves in one full rotation of the disc is

Which two motions are considered to be combined for motion in plane ?

A body starts from rest from the origin with an acceleration of $6 \;m / s^2$ along the $x$-axis and $8\; m / s^2$ along the $y$-axis. Its distance from the origin after $4\; seconds$ will be

A particle moves in space along the path $z = ax^3 + by^2$ in such a way that $\frac{dx}{dt} = c = \frac{dy}{dt}.$ Where $a, b$ and $c$ are contants. The acceleration of the particle is