The velocity-displacement graph of a particle | vedclass

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

Question

(C) From the given graph,the velocity $v$ as a function of displacement $x$ is a straight line with a negative slope.Using the equation of a line $y =

Vedclass · Accepted Answer

Vedclass · Answer

(C) From the given graph,the velocity $v$ as a function of displacement $x$ is a straight line with a negative slope.Using the equation of a line $y = mx + c$,we have:$v = -\left(\frac{v_{0}}{x_{0}}\right)x + v_{0}$We know that acceleration $a$ is given by:$a = v \frac{dv}{dx}$First,find the derivative $\frac{dv}{dx}$:$\frac{dv}{dx} = -\frac{v_{0}}{x_{0}}$Now,substitute $v$ and $\frac{dv}{dx}$ into the expression for $a$:$a = \left[-\left(\frac{v_{0}}{x_{0}}\right)x + v_{0}\right] \left[-\frac{v_{0}}{x_{0}}\right]$$a = \left(\frac{v_{0}}{x_{0}}\right)^{2}x - \frac{v_{0}^{2}}{x_{0}}$This equation represents a straight line with a positive slope $\left(\frac{v_{0}}{x_{0}}\right)^{2}$ and a negative intercept $-\frac{v_{0}^{2}}{x_{0}}$. Looking at the options,graph $C$ represents a linear relationship where $a$ increases with $x$ starting from a negative value,which matches our derived equation.

The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by:

Similar Questions

The motion of an airplane is represented by a velocity-time graph as shown below. The distance covered by the airplane in the first $30.5 \ s$ is . . . . . . $km$.

Explain instantaneous velocity.

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time-axis as shown in the figure. The ratio of their respective velocities is:

The figure shows the $x-t$ plot of a particle in one-dimensional motion. Three different equal intervals of time are shown. In which interval is the average speed greatest,and in which is it the least? Give the sign of average velocity for each interval.

If a steel ball is dropped from a height onto a marble floor,what will the velocity-time graph look like?

Vedclass Test Series

Exam Paper Generator

Online Exam Module