The velocity (v) - distance (x) graph is show | vedclass

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

Question

(B) The equation of the $v$ vs $x$ graph is a straight line with a negative slope and a positive intercept on the $v$-axis:$v = C_1 - C_2 x$, where $C

Vedclass · Accepted Answer

Vedclass · Answer

(B) The equation of the $v$ vs $x$ graph is a straight line with a negative slope and a positive intercept on the $v$-axis:$v = C_1 - C_2 x$, where $C_1$ and $C_2$ are positive constants.The acceleration $a$ is given by the relation:$a = v \frac{dv}{dx}$Substituting the expression for $v$ and its derivative $\frac{dv}{dx} = -C_2$:$a = (C_1 - C_2 x) 	imes (-C_2)$$a = C_2^2 x - C_1 C_2$This equation is of the form $a = mx + c$, where the slope $m = C_2^2$ (positive) and the intercept $c = -C_1 C_2$ (negative).Thus, the graph of $a$ versus $x$ is a straight line with a positive slope and a negative intercept on the $a$-axis, which corresponds to option $B$.

The velocity $(v)$ - distance $(x)$ graph is shown in the figure. Which graph represents the acceleration $(a)$ versus distance $(x)$ variation of this system?

Similar Questions

Draw the $x-t$ graph for positive acceleration.

The acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is

The velocity-time graph of a body moving along a straight line is shown in the figure. The ratio of the average velocities during the time intervals $t_1$ and $t_2$ 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 $, m$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module