Question

The odometer of the car reads 2000 km at the start of the trip and 2400 km at the end of the trip. If the trip took 8 h, calculate the average speed of the car in $km{h^{ - 1}}$ and $ m{s^{ - 1}}$.
A. 50 km/h or 13.9 m/s
B. 40 km/h or 12.5 m/s
C. 50 km/h or 12.5 m/s
D. 40 km/h or 13.9 m/s

Answer 1

Hint: for this question we first draw using the information given in the question. Then need to write the expression for average speed that is \[Average{\text{ }}Speed = \dfrac{{Total{\text{ Distance}}{\text{ }}Covered}}{{Total{\text{ }}Time{\text{ }}taken}}\]. After that, we will find the total distance as $2400km - 2000km = 400km$ and the total time as 8h as given in the question. Then we substitute these values and get the average speed 50 km/h and then convert it to m/s.

Complete Step-by-Step solution:
We know that an odometer is an instrument used to measure the distance traveled by a vehicle. In this question, the odometer is showing 2000 km at the start of the trip and is showing 2400 km at the end of the trip.
So the total distance traveled by car on the trip is $2400km - 2000km = 400km$
It is given that the total time taken to complete the trip is 8 h as shown in figure 1.

Figure 1

We know that
\[Average{\text{ }}Speed = \dfrac{{Total{\text{ Distance}}{\text{ }}Covered}}{{Total{\text{ }}Time{\text{ }}taken}}\]
\[ \Rightarrow \dfrac{{Total{\text{ }}Distance{\text{ }}Covered}}{{Total{\text{ }}Time{\text{ }}taken}} = \dfrac{{400km}}{{8h}}\]
\[ \Rightarrow Average{\text{ }}Speed = 50\dfrac{{km}}{h}\]
Hence the average speed in km/h is 50 but we are also asked to find the average speed in m/s for that
We can write$ \Rightarrow 50\dfrac{{km}}{h} = 50\dfrac{{1000m}}{{3600s}}$
 $ \Rightarrow 50\dfrac{{km}}{h} = 50\dfrac{{1000m}}{{3600s}}$
$ \Rightarrow 50\dfrac{{1000m}}{{3600s}} = \dfrac{{125m}}{{9s}}$
$ \Rightarrow 13.88{m}/{s} \simeq 13.9$${m}/{s}$
So we are getting the average speed of the car as 50 km/h or 13.9 m/s.

Note: In these types of questions, we first need to know the uses of odometer and speedometer. Then we need to know the relation between the average speed, distance, and time. Then we find the values of the variable needed in the formula and solve for the answer. We also need to know how to convert km/h to m/s and m/min.