Question

The average speed of a bicycle, an athlete and a car are \[18\,{\text{km}}\,{{\text{h}}^{ - 1}}\] , \[7\,{\text{m}}\,{{\text{s}}^{ - 1}}\] and \[2\,{\text{km}}\,{\text{mi}}{{\text{n}}^{ - 1}}\] , respectively. Which of the three is the fastest and which is the slowest?
A. Car is the fastest, bicycle is the slowest
B. Bicycle is the fastest, car is the slowest
C. Car is the fastest, athlete is the slowest
D. Athlete is the fastest, bicycle is the slowest

Answer 1

Hint: First of all, before comparing their speeds, we will convert them into meter per second. After we are done with that, we will make the comparison to get the result.

Complete step by step answer:
In the given question, we are supplied with the following data:
We are given the average speeds of a bicycle, an athlete and a car, which are given as \[18\,{\text{km}}\,{{\text{h}}^{ - 1}}\] , \[7\,{\text{m}}\,{{\text{s}}^{ - 1}}\] and \[2\,{\text{km}}\,{\text{mi}}{{\text{n}}^{ - 1}}\] . We are asked to find out which among the following is the fastest and which one among the following is the slowest.

To begin with, as we can see that three of them have got their own velocities, but they are represented in different units. Until the units are the same, we cannot compare them. Speed is termed as the distance per unit time. Larger is the distance covered per unit time, greater is the speed of that object. Let us convert the unit of speed of the bicycle and the car into meters per second.

Speed of the bicycle is \[18\,{\text{km}}\,{{\text{h}}^{ - 1}}\] .
$18\,{\text{km}}\,{{\text{h}}^{ - 1}} \\
\Rightarrow \dfrac{{18\,{\text{km}}}}{{1\,{\text{h}}}} \\
\Rightarrow\dfrac{{18 \times 1000\,{\text{m}}}}{{60 \times 60\,{\text{s}}}} \\
\Rightarrow5\,{\text{m}}\,{{\text{s}}^{ - 1}} \\$
Therefore, the speed of the bicycle is \[5\,{\text{m}}\,{{\text{s}}^{ - 1}}\] .

Speed of the car is \[2\,{\text{km}}\,{\text{mi}}{{\text{n}}^{ - 1}}\] .
$2\,{\text{km}}\,{\text{mi}}{{\text{n}}^{ - 1}} \\
\Rightarrow\dfrac{{2\,{\text{km}}}}{{1\,\min }} \\
\Rightarrow\dfrac{{2 \times 1000\,{\text{m}}}}{{60\,{\text{s}}}} \\
\Rightarrow 33.33\,{\text{m}}\,{{\text{s}}^{ - 1}} \\$
Therefore, the speed of the car is \[33.33\,{\text{m}}\,{{\text{s}}^{ - 1}}\] .
As now all the units are the same, we can compare their velocities.
\[\because 5\,{\text{m}}\,{{\text{s}}^{ - 1}} < 7\,{\text{m}}\,{{\text{s}}^{ - 1}} < 33.33\,{\text{m}}\,{{\text{s}}^{ - 1}}\]
\[\therefore {v_{{\text{bicycle}}}} < {v_{{\text{athlete}}}} < {v_{{\text{car}}}}\]
Hence, a car is the fastest, a bicycle is the slowest.

The correct option is A.

Note: While solving this problem, most of the students tend to make mistakes while in a hurry. They don’t convert into the same units; they compare by just looking at it. This is absolutely wrong. If we didn’t convert, then the car would have the slowest and bicycle would have been the fastest. It is mandatory to convert into the same units.