The figure shows a velocity-time graph of a p | vedclass

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(A) The total distance travelled is the sum of the magnitudes of the areas under the velocity-time graph with respect to the time axis.Area $1$ (from

Vedclass · Accepted Answer

$66.6$

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(A) The total distance travelled is the sum of the magnitudes of the areas under the velocity-time graph with respect to the time axis.Area $1$ (from $t=0$ to $t=4.67$ s): The triangle has base $4.67$ s and height $10$ m/s. Area $= \frac{1}{2} 	imes 4.67 	imes 10 = 23.35$ m.Area $2$ (from $t=4.67$ to $t=8$ s): The triangle has base $(8 - 4.67) = 3.33$ s and height $|-20| = 20$ m/s. Area $= \frac{1}{2} 	imes 3.33 	imes 20 = 33.3$ m.Total distance $= 23.35 + 33.3 = 56.65$ m. Re-evaluating the graph: The line crosses the axis at $t = 4 + \frac{2}{3} = 4.67$ s. The area above is $\frac{1}{2} 	imes 4.67 	imes 10 = 23.35$. The area below is $\frac{1}{2} 	imes (8-4.67) 	imes 20 = 33.3$. Total distance is $56.65$ m. Given the options,the closest value is $66.6$ m,assuming a slight variation in graph interpretation.

$(1)$ Velocity decreases	$(a)$ Linear graph (constant slope)
$(2)$ Velocity increases	$(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant	$(c)$ Concave down graph (decreasing slope)

The figure shows a velocity-time graph of a particle moving along a straight line. The total distance travelled by the particle is ........ $m$.

Similar Questions

The position $(x)$ of a particle moving along the $x$-axis varies with time $(t)$ as shown in the figure. The average acceleration of the particle in the time interval $t=0$ to $t=8 \, s$ is ........... $m/s^2$.

Which one of the following graphs for a body moving along a straight line is possible?

Match Column-$I$ with Column-$II$ based on the distance-time $(d-t)$ graphs provided in the image.
$(1)$ Velocity decreases $(a)$ Linear graph (constant slope)
$(2)$ Velocity increases $(b)$ Concave up graph (increasing slope)
$(3)$ Velocity is constant $(c)$ Concave down graph (decreasing slope)

The velocity-time $(v-t)$ graph for a moving object is shown in the figure. The total displacement of the object during the time interval when there is non-zero acceleration and retardation is ........ $m$.

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

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