Question

The odometer of the bike reads 1600 km at the start of the trip and 2000 km at the end of the trip. If the bike took 16 h, calculate the average speed of the bike in km/h and m/s.

Answer 1

Hint: We have been asked to find the answer in km/h and m/s but we have been given the parameters only in km (kilometre) and h (hour). Also, we have been given two different readings for distance. Average speed is total distance travelled upon total time. So, we will be calculating the value of distance that should be taken to calculate the average speed of the bike.

Formula used: \[{{V}_{avg}}=\dfrac{S}{t}\]

Complete step by step answer:
We know that average speed is the ratio of total distance travelled by a body to the total time taken to cover the same distance.
So, the total distance travelled will be initial reading by the odometer subtracted from final reading
Therefore,
\[S=2000-1600=400\]
\[\therefore S=400km\]
We have time \[t=16h\]
So, using the formula
\[{{V}_{avg}}=\dfrac{S}{t}\]
After substituting the given values in above formula
We get,
\[{{V}_{avg}}=\dfrac{400}{16}\]
\[\therefore {{V}_{avg}}=25km/h\]
Now to find the answers in m/s we have two different ways. We can convert our obtained answer directly by converting the units in CGS or we can convert the given parameters in CGS units and then follow the same process. The later method would be time consuming. So, it is better to convert the obtained answer in m/s. To do that we will have to convert the units in m/s.
So, we know
1 km = 1000m
Similarly,
1 hour = 3600 seconds.
Therefore,
\[{{V}_{avg}}=25\times \dfrac{1000}{3600}\]
\[\therefore {{V}_{avg}}=25km/h\]
If we must, we can round up the answer to,
\[{{V}_{avg}}=7m/s\]

Additional Information: Here, we have been asked to find the average speed. Therefore, we took the difference i.e. the total distance travelled to calculate the speed. However, if it asked to find the instantaneous speed we must know the distance travelled at a specific instant. So, students must be careful as to what is asked in the question.
Odometer is an instrument used in bikes and other wheeled vehicles to measure the distance travelled.

Note: Students must be careful while converting the units from SI to CGS. We must always write the answer upto the fourth decimal place. This is done to make sure our answer is closest to the required answer. However, if the answer is rounded up we must do the same.