Question

A body travels \[20\;{\rm{km}}\]east and made a right turn to travel \[30\;{\rm{km}}\] then the total time spent is \[5\;{\rm{hr}}\], then find average velocity and speed.

Answer 1

Hint: The above problem can be resolved using kinematic variables like the average and the average velocity. The average velocity can be calculated by calculating the shortest distance covered by the body. And in this case, the path is formed in the form of a triangle; and the shortest distance is taken by calculating the value of the hypotenuse of the triangle.

Complete step by step solution:
Given:
The distance travelled in the east is, \[{d_1} = 20\;{\rm{km}}\].
The distance covered after taking right is, \[{d_2} = 30\;{\rm{km}}\].
The time taken for the journey is, \[t = 5\;{\rm{hr}}\].
The expression for the average velocity is
 \[{v_{av.}} = \dfrac{d}{t}\]
Here d is the magnitude of displacement and its value is,
\[\begin{array}{l}
d = \sqrt {d_1^2 + d_2^2} \\
d = \sqrt {{{\left( {20\;{\rm{km}}} \right)}^2} + {{\left( {30\;{\rm{km}}} \right)}^2}} \\
d = 25\;{\rm{km}}
\end{array}\]
Solve by substituting the values as,
\[\begin{array}{l}
{v_{av.}} = \dfrac{d}{t}\\
\Rightarrow {v_{av.}} = \dfrac{{25\;{\rm{km}}}}{{5\;{\rm{hr}}}}\\
\Rightarrow {v_{av.}} = 5\;{\rm{km/h}}
\end{array}\]
Now, the average speed is,
\[\begin{array}{l}
s = \dfrac{{{d_1} + {d_2}}}{t}\\
\Rightarrow s = \dfrac{{20\;{\rm{km}} + 30\;{\rm{km}}}}{{5\;{\rm{h}}}}\\
\Rightarrow s = 10\;{\rm{km/h}}
\end{array}\]

Therefore, the average velocity is \[5\;{\rm{km/h}}\] and average speed is \[10\;{\rm{km/h}}\].

Note: Try to understand the concept and mathematical relation for average velocity and average speed must be remembered to resolve the above problem. The average velocity in any duration of the journey is calculated by analysing the shortest length of the path the entity covers. Moreover, this shortest distance is then divided by the time interval to obtain the average velocity's final value. The average speed is that variable whose value can be calculated by taking the sum of all the distances covered and then dividing the result by time interval to obtain the desired value of average speed.