Question

A dancer is demonstrating dance steps along a straight line.The position – time graph is given above. Find the average speed of the dance step depicted by CD.

 A. \[1\;{\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}\]
B. \[1.33\;{\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}\]
C. \[2.67\;{\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}\]
D. \[0.89\;{\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}\]

Answer 1

Hint: The given problem is resolved using the concepts and applications of average speed. Moreover, the frequent analysis of the given data is required to resolve the problem completely for the given time interval.

Complete step by step answer:
Given:
The dancer demonstrating the dance steps along a specific path for the given time interval, for which the position- time graph is shown.
From the given position- time graph, the distance for the dance step CD is d = 4m.
And the time taken to cover the distance is, t = 5 s – 3.5 s = 1.5 s.
The average speed is given as,
\[v = \dfrac{d}{t}\]
Substituting values,
\[\begin{array}{l}
v = \dfrac{d}{t}\\
v = \dfrac{{4\;{\rm{m}}}}{{1.5\;{\rm{s}}}}\\
v = 2.67\;{\rm{m/s}}
\end{array}\]
Therefore, the required value of average speed for the dance step is 2.67 m/s

Note:
To resolve the given problem, the fundamental relations of kinematic equations is to be known along with the proper knowledge of terms like Average speed, displacement and many more. Moreover, the application of Speed – time is very important to overcome the like conditions as a given problem. It is important to note the accurate distance covered along with the time required to cover the distance, to conclude the problem.