A particle moves in a straight line with reta | vedclass

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

Question

(A) Given that retardation $a$ is proportional to displacement $x$,so $a = -kx$ (where $k$ is a positive constant).Using the relation $a = v \frac{dv}

Vedclass · Accepted Answer

$x^2$

Vedclass · Answer

(A) Given that retardation $a$ is proportional to displacement $x$,so $a = -kx$ (where $k$ is a positive constant).Using the relation $a = v \frac{dv}{dx}$,we have $v \frac{dv}{dx} = -kx$.Integrating both sides: $\int v dv = \int -kx dx$.This gives $\frac{v^2}{2} = -\frac{kx^2}{2} + C$.At $x = 0$,let the initial velocity be $u$,so $C = \frac{u^2}{2}$.Thus,$\frac{v^2}{2} = \frac{u^2}{2} - \frac{kx^2}{2}$,which implies $u^2 - v^2 = kx^2$.The loss in kinetic energy is $\Delta K = \frac{1}{2}m(u^2 - v^2) = \frac{1}{2}m(kx^2)$.Since $m$ and $k$ are constants,the loss in kinetic energy is proportional to $x^2$.

$A$ particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:

Similar Questions

An artificial pacemaker is implanted subcutaneously and connected to the heart in patients:

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$ and if $px^2+qx+r=0$ has roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$,then $r$ is equal to

Which one of the following elements is not an essential micronutrient for plant growth?

Give the number of electrons in the species $H_{2}^{+}$,$H_{2}$,and $O_{2}^{+}$.

The length of the subtangent at any point of the curve $x^m y^n = a^{m+n}$ is proportional to -

Vedclass Test Series

Exam Paper Generator

Online Exam Module