The curve between net force and time is shown | vedclass

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

Question

(D) From Newton's second law,$F = ma = m(dv/dt)$,which implies $dv = (F/m) dt$.Integrating both sides,the change in velocity $\Delta v = \int (F/m) dt

Vedclass · Accepted Answer

Vedclass · Answer

(D) From Newton's second law,$F = ma = m(dv/dt)$,which implies $dv = (F/m) dt$.Integrating both sides,the change in velocity $\Delta v = \int (F/m) dt = (1/m) \int F dt$.Since the particle starts from rest,the velocity $v(t)$ at any time $t$ is proportional to the area under the force-time graph up to that time.$1$. Initially,$F$ is constant and non-zero,so the acceleration $a = F/m$ is constant. This means the velocity increases linearly with time $(v = at)$.$2$. During the interval where $F$ increases and then decreases (the triangular pulse),the acceleration $a$ also increases and decreases. Consequently,the slope of the velocity-time graph $(dv/dt = a)$ increases and then decreases,resulting in a curved (concave up) shape for the $v-t$ graph.$3$. After the pulse,$F$ returns to its initial constant value,so the acceleration becomes constant again,and the velocity-time graph becomes a straight line with the same slope as the initial part.Comparing this behavior with the given options,Graph $D$ correctly shows a linear increase,followed by a curved section where the slope increases and decreases,and finally a linear increase with the original slope.

The curve between net force and time is shown. Initially,the particle is at rest. Which of the following best represents the resulting velocity-time graph of the particle?

Similar Questions

$A$ man balances himself in a horizontal position by pushing his hands and feet against two parallel walls. His centre of mass lies midway between the walls. The coefficients of friction at the walls are equal. Which of the following is not correct?

$A$ spring-block system is placed on a rough horizontal floor. The block is pulled towards the right to give the spring an elongation $x_0$ such that $\frac{\mu mg}{K} < x_0 < \frac{2\mu mg}{K}$,and then released. Which of the following statements is correct?

$A$ ball connected with a string is released at an angle of $45^{\circ}$ with the vertical,as shown in the figure. If the mass of the box is equal to the mass of the ball,the acceleration of the box at this instant will be:

$A$ $500 \, kg$ horse pulls a cart of mass $1500 \, kg$ along a level road with an acceleration of $1 \, m/s^2$. If the coefficient of sliding friction is $0.2$,then the force exerted by the horse in the forward direction is ......... $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module