A particle of mass m is at rest at the origin | vedclass

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

Question

(D) Given,force $F(t) = F_0e^{-bt}$.According to Newton's second law,$F = ma = m \frac{dv}{dt}$.So,$m \frac{dv}{dt} = F_0e^{-bt}$.Integrating both sid

Vedclass · Accepted Answer

Vedclass · Answer

(D) Given,force $F(t) = F_0e^{-bt}$.According to Newton's second law,$F = ma = m \frac{dv}{dt}$.So,$m \frac{dv}{dt} = F_0e^{-bt}$.Integrating both sides with respect to time $t$ from $0$ to $t$:$\int_0^v dv = \int_0^t \frac{F_0}{m} e^{-bt} dt$.$v(t) = \frac{F_0}{m} \left[ \frac{e^{-bt}}{-b} ight]_0^t$.$v(t) = \frac{F_0}{m} \left( \frac{e^{-bt} - 1}{-b} ight) = \frac{F_0}{mb} (1 - e^{-bt})$.As $t 	o 0$,$v(t) 	o 0$.As $t 	o \infty$,$v(t) 	o \frac{F_0}{mb}$.The function $v(t) = \frac{F_0}{mb} (1 - e^{-bt})$ represents an increasing curve that asymptotically approaches the value $\frac{F_0}{mb}$.This corresponds to the curve shown in option $D$.

$A$ particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$-direction. Its speed $v(t)$ is depicted by which of the following curves?

Similar Questions

$A$ ball of mass $0.2 \, kg$ moves with a velocity of $20 \, m/s$ and it stops in $0.1 \, s$; then the force on the ball is ........... $N$.

$A$ force on an object of mass $100\, g$ is $(10 \hat{i}+5 \hat{j})\ N$. The position of that object at $t= 2\ s$ is $(a \hat{i}+b \hat{j})\, m$ after starting from rest. The value of $\frac{a}{b}$ will be..........

$A$ wooden block,initially at rest on the ground,is pushed by a force which increases linearly with time $t$. Which of the following curves best describes the acceleration of the block with time?

$A$ body,under the action of a force $\vec F = 6\hat i - 8\hat j + 10\hat k$,acquires an acceleration of $1\, m/s^2$. The mass of this body must be

The figure represents the momentum-time $(p-t)$ curve for a particle moving along an axis under the influence of a force. Identify the regions on the graph where the magnitude of the force is maximum and minimum,respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module