The speed-time graph of a particle moving alo | vedclass

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

Question

(C) The distance traversed by the particle is equal to the area under the speed-time graph.For the interval $t=2\;s$ to $t=5\;s$:The speed $v$ at time

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) The distance traversed by the particle is equal to the area under the speed-time graph.For the interval $t=2\;s$ to $t=5\;s$:The speed $v$ at time $t$ is given by $v = at$. Since $v=12\;m/s$ at $t=5\;s$,the acceleration $a_1 = 12/5 = 2.4\;m/s^2$.At $t=2\;s$,$v_2 = 2.4 	imes 2 = 4.8\;m/s$.At $t=5\;s$,$v_5 = 12\;m/s$.The distance $s_1$ is the area of the trapezoid from $t=2$ to $t=5$:$s_1 = \frac{1}{2} 	imes (v_2 + v_5) 	imes (5-2) = \frac{1}{2} 	imes (4.8 + 12) 	imes 3 = \frac{1}{2} 	imes 16.8 	imes 3 = 25.2\;m$.For the interval $t=5\;s$ to $t=6\;s$:The deceleration $a_2$ is the slope of the line from $t=5$ to $t=10$,which is $a_2 = (0-12)/(10-5) = -2.4\;m/s^2$.At $t=6\;s$,the speed $v_6 = v_5 + a_2 	imes (6-5) = 12 + (-2.4) 	imes 1 = 9.6\;m/s$.The distance $s_2$ is the area of the trapezoid from $t=5$ to $t=6$:$s_2 = \frac{1}{2} 	imes (v_5 + v_6) 	imes (6-5) = \frac{1}{2} 	imes (12 + 9.6) 	imes 1 = \frac{1}{2} 	imes 21.6 = 10.8\;m$.Total distance $s = s_1 + s_2 = 25.2 + 10.8 = 36\;m$.

The speed-time graph of a particle moving along a fixed direction is shown in the figure. Obtain the distance traversed by the particle in $m$ between $t=2\;s$ to $6\;s$.

Similar Questions

What does $\dot x$ represent?

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.

During which time interval is the particle described by these position graphs at rest?

Fill in the blanks:
$(a)$ The path length is always ............ .
$(b)$ The slope of the velocity-time graph for an object moving with acceleration is ............ .
$(c)$ If the velocity-time graph is parallel to the time-axis,the object is ............ .

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module