Question

If the average speed of a lion for a day is $1296\,{\text{km/day}}$. Then its speed can also be expressed as
A. $108\,{\text{km/hr}}$
B. $15\,{\text{m/s}}$
C. $30\,{\text{m/s}}$
D. $72\,{\text{km/hr}}$

Answer 1

Use the proper conversion factors for the conversion of kilometer into meter, day into hours and day into seconds. Convert the average speed of the lion for a day into the units kilometer per hour as well as meter per second and check which of the options given is correct and equivalent to the given speed of the lion.

Complete step by step answer:
We have given that the average speed of the lion for a day is $1296\,{\text{km/day}}$.
${v_{avg}} = 1296\,{\text{km/day}}$
One kilometer is equal to 1000 meter.
$1\,{\text{km}} = {\text{1000}}\,{\text{m}}$
One day has 24 hours, one hour has 60 minutes and one minute has 60 seconds.
$1\,{\text{day}} = 24\,{\text{hr}}$
$\Rightarrow 1\,{\text{hr}} = 60\,\min$
$\Rightarrow 1\,{\text{min}} = 60\,s$

Convert the average speed of the lion in kilometers per hour.
${v_{avg}} = \left( {1296\,\dfrac{{{\text{km}}}}{{{\text{day}}}}} \right)\left( {\dfrac{{1\,{\text{day}}}}{{24\,{\text{hr}}}}} \right)$
$\Rightarrow {v_{avg}} = 54\,\dfrac{{{\text{km}}}}{{{\text{hr}}}}$
Hence, the average speed of the lion in kilometer per hour is $54\,{\text{km/hr}}$ and not $108\,{\text{km/hr}}$ or $72\,{\text{km/hr}}$.Hence, the options A and D are incorrect.

Convert the unit of average speed of the lion in meters per second.
${v_{avg}} = \left( {1296\,\dfrac{{{\text{km}}}}{{{\text{day}}}}} \right)\left( {\dfrac{{{{10}^3}\,{\text{m}}}}{{1\,{\text{km}}}}} \right)\left[ {\left( {\dfrac{{1\,{\text{day}}}}{{24\,{\text{hr}}}}} \right)\left( {\dfrac{{1\,{\text{hr}}}}{{60\,{\text{min}}}}} \right)\left( {\dfrac{{1\,{\text{min}}}}{{60\,{\text{s}}}}} \right)} \right]$
$\therefore {v_{avg}} = 15\,{\text{m/s}}$
Therefore, the average speed of the lion in meter per second is $15\,{\text{m/s}}$ and not $30\,{\text{m/s}}$.Hence, the option C is incorrect.

Hence, the correct option is B.

Additional information:
The average speed of an object is the ratio of the total distance travelled by the object to the time required for the travel.
${v_{avg}} = \dfrac{d}{t}$
Here, $d$ is the total distance travelled by the object and $t$ is the total time required for travelling the same distance.

Note: Use proper conversion factors for the conversion of kilometer to meter, day to hours and day to seconds to convert the speed of lion from kilometer per day to kilometer per hour and meter per second. If the conversion factors are not taken correctly, we will not have the correct answer at the end of the solution.