The velocity (v) versus displacement (x) plot | vedclass

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

Question

(D) The acceleration $a$ is given by $a = v \frac{dv}{dx}$.From the given graph,the velocity $v$ is a linear function of displacement $x$.For the inte

Vedclass · Accepted Answer

Vedclass · Answer

(D) The acceleration $a$ is given by $a = v \frac{dv}{dx}$.From the given graph,the velocity $v$ is a linear function of displacement $x$.For the interval $0 \le x \le 100$,the slope is positive. Let $v = kx$ (where $k > 0$). Then,$a = v \frac{dv}{dx} = (kx)(k) = k^2 x$. This shows that $a$ increases linearly with $x$ in this interval.For the interval $100 \le x \le 200$,the slope is negative. Let $v = -k(x - 200) = -kx + 200k$. Then,$a = v \frac{dv}{dx} = (-kx + 200k)(-k) = k^2 x - 200k^2$. This shows that $a$ increases linearly with $x$ in this interval,but with a negative intercept.Comparing this with the given options,the graph that shows a positive linear increase in acceleration for the first part and a positive linear increase with a negative value for the second part is option $D$.

The velocity $(v)$ versus displacement $(x)$ plot of a body moving along a straight line is as shown in the graph. The corresponding plot of acceleration $(a)$ as a function of displacement $(x)$ is

Similar Questions

$A$ train starting from rest accelerates uniformly for $100\,s,$ then comes to a stop with a uniform retardation in the next $200\,s.$ During the motion,it covers a distance of $3\,km.$ Choose the wrong option.

The graph between the displacement $x$ and time $t$ for a particle moving in a straight line is shown in the figure. Determine the sign of the acceleration of the particle for the intervals $OA$,$AB$,$BC$,and $CD$ respectively.

The displacement $x$ of a particle in a straight line motion is given by $x = 1 - t - t^2$. The correct representation of the motion is $..............$.

The variation of velocity of a particle moving along a straight line with time is illustrated in the following figure. The distance travelled by the particle in $4 \, s$ is: (in $, m$)

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module