An object starts from rest and is acted upon | vedclass

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

Question

(A) The $F-x$ graph is a straight line. The equation of the line is $F = x 	an \alpha - F_0$.According to Newton's second law,$F = ma = m v \frac{dv}

Vedclass · Accepted Answer

$\frac{2 F_0}{	an \alpha}$

Vedclass · Answer

(A) The $F-x$ graph is a straight line. The equation of the line is $F = x 	an \alpha - F_0$.According to Newton's second law,$F = ma = m v \frac{dv}{dx}$.Thus,$m v \frac{dv}{dx} = x 	an \alpha - F_0$.Integrating both sides with respect to $x$ from $x=0$ to $x=x_f$ (where velocity $v$ changes from $0$ to $0$):$\int_{0}^{0} m v \, dv = \int_{0}^{x_f} (x 	an \alpha - F_0) \, dx$.The left side is $0$,so:$0 = \left[ \frac{x^2}{2} 	an \alpha - F_0 x ight]_{0}^{x_f}$.$0 = \frac{x_f^2}{2} 	an \alpha - F_0 x_f$.Since $x_f 
eq 0$,we divide by $x_f$:$0 = \frac{x_f}{2} 	an \alpha - F_0$.$x_f = \frac{2 F_0}{	an \alpha}$.

An object starts from rest and is acted upon by a variable force $F$ as shown in the figure. If $-F_0$ is the initial value of the force at $x=0$,then the position of the object where it again comes to rest will be:

Similar Questions

Arrange the four graphs in descending order of total work done; where $W_{1}, W_{2}, W_{3}$ and $W_{4}$ are the work done corresponding to Figure-$a$,Figure-$b$,Figure-$c$ and Figure-$d$ respectively.

$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in newton $(N)$ and $x$ is in metre $(m)$. The work done by the force in moving the object from $x = 0$ to $x = 6\,m$ is......$J$.

$A$ force $(3x^2 + 2x - 5) \text{ N}$ displaces a body from $x = 2 \text{ m}$ to $x = 4 \text{ m}$. The work done by this force is .......... $J$.

The work done by a force $\vec{F} = -5x^4 \hat{i} \text{ N}$ in displacing a body from $x = 2 \text{ m}$ to $x = -2 \text{ m}$ is: (in $\text{ J}$)

Force acting on a body of mass $1 \ kg$ is related to its position $x$ as $F = x^3 - 3x \ N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ......... $m/s$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module