Question

Find the average velocity of an athlete who runs 1500 m in 4 minutes, show in m/s and km/h.

Answer 1

Hint: As the average velocity is the ratio of displacement by time, so, we will divide the value of displacement by time. Firstly, we will convert the unit of time into seconds to compute the value in terms of m/s. Then we will convert the unit into km/hr.
Formula used:
\[{{v}_{avg}}=\dfrac{\Delta x}{\Delta t}\]

Complete answer:
The average velocity is the ratio of the displacement by time. The formula for computing the same is given as follows.
\[{{v}_{avg}}=\dfrac{\Delta x}{\Delta t}\]
Where \[\Delta x\]is the change in the displacement and \[\Delta t\]is the change in time.
From the given information, we have the data as follows.
The distance covered by an athlete, \[d=1500m\]
The time taken by an athlete, \[t=4\min \]
Firstly, we will convert the unit of time from minutes into seconds.
As 1 minute equals 60 seconds, so,
\[\begin{align}
  & 4\min =4\times 60\sec \\
 & \Rightarrow 4\min =240\sec \\
\end{align}\]
As the distance is in meters, so, no need to change at this point.
Now, we will compute the average velocity in terms of meter per second.
Consider the formula
\[{{v}_{avg}}=\dfrac{\Delta x}{\Delta t}\]
Substitute the values in the above formula.
\[\begin{align}
  & {{v}_{avg}}=\dfrac{1500-0}{240-0} \\
 & \Rightarrow {{v}_{avg}}=\dfrac{1500}{240} \\
 & \therefore {{v}_{avg}}=\dfrac{25}{4} \\
\end{align}\]
Therefore, the average velocity in terms of meter per sec is 6.25 m/s.
Now, we will convert the unit of average velocity from meter per second into km per hour.
So, we have,
\[\begin{align}
  & {{v}_{avg}}=\dfrac{25}{4}\times \dfrac{3600}{1000} \\
 & \Rightarrow {{v}_{avg}}=\dfrac{900}{40} \\
 & \therefore {{v}_{avg}}=\dfrac{90}{4} \\
\end{align}\]
Therefore, the average velocity in terms of km per hour is 22.5 km/hr.
\[\therefore \]The average velocity in terms of m/s is \[6.25{m}/{s}\;\] and in terms of km/hr is \[22.5{km}/{hr}\;\].

Note:
The question is all about the units of the parameters used, that is, the unit conversion. Firstly, the unit of the time should be converted into seconds from the minutes to represent the result in terms of m/sec. Then, again the unit should be converted in terms of km/hr. The unit conversion method should be known to solve this problem.