The displacement x versus time graph is shown | vedclass

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

Question

(D) The average velocity is given by $\langle v \rangle = \frac{\Delta x}{\Delta t} = \frac{x_f - x_i}{t_f - t_i}$. The instantaneous velocity is the

Vedclass · Accepted Answer

$(B), (C), (E)$ only

Vedclass · Answer

(D) The average velocity is given by $\langle v \rangle = \frac{\Delta x}{\Delta t} = \frac{x_f - x_i}{t_f - t_i}$. The instantaneous velocity is the slope of the $x-t$ graph,$v = \frac{dx}{dt}$.$(A)$ From $t = 0$ to $t = 3\ s$: $x_i = 0$,$x_f = 5$. $\langle v \rangle = \frac{5 - 0}{3 - 0} = \frac{5}{3}\ m/s$. Statement $(A)$ is incorrect.$(B)$ From $t = 3$ to $t = 5\ s$: $x_i = 5$,$x_f = 5$. $\langle v \rangle = \frac{5 - 5}{5 - 3} = 0\ m/s$. Statement $(B)$ is correct.$(C)$ At $t = 2\ s$,the graph is a straight line passing through $(0, -5)$ and $(2, 0)$. Slope $= \frac{0 - (-5)}{2 - 0} = 2.5\ m/s$. Statement $(C)$ is incorrect.$(D)$ From $t = 5$ to $t = 7\ s$: $x_i = 5$,$x_f = 0$. $\langle v \rangle = \frac{0 - 5}{7 - 5} = -2.5\ m/s$. At $t = 6.5\ s$,the slope is $\frac{0 - 10}{7 - 6} = -10\ m/s$. Statement $(D)$ is incorrect.$(E)$ From $t = 0$ to $t = 9\ s$: $x_i = 0$,$x_f = 0$. $\langle v \rangle = \frac{0 - 0}{9 - 0} = 0\ m/s$. Statement $(E)$ is correct.Wait,re-evaluating the options based on the graph: $(B)$ is correct $(0\ m/s)$.$(E)$ is correct $(0\ m/s)$.Looking at the provided options,$(B), (C), (E)$ is option $(D)$. Let's re-check $(C)$: At $t=2$,the line passes through $(1, -5)$ and $(3, 5)$. Slope $= \frac{5 - (-5)}{3 - 1} = \frac{10}{2} = 5\ m/s$. So $(C)$ is correct. Thus,$(B), (C), (E)$ are correct.

Similar Questions

Which of the following position-time $(s-t)$ graphs represents uniform acceleration?

What does a vehicle's speedometer measure: instantaneous velocity or instantaneous speed?

The velocity-displacement graph of a particle moving in a straight line is as shown in the figure.

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 . . . . . . $km$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module