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Rajeev went from Delhi to Chandigarh on his motorbike. The odometer of that read $4200\;km$ at the start of the trip and $4460\;km$ at the end of his trip. If Rajeev took $4\;h$ $20\min $ to complete his trip, then find the average speed and average velocity in $km/h$ as well as in $m/s$.

Last updated date: 20th Jun 2024
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Hint: - The odometer is a device used to determine the distance travelled by a vehicle. It is fitted right next to the speedometer. To get the distance travelled by car in between the given time determine the difference in readings of the odometer. To get the average speed divide the total distance travelled by car by the total time taken.
Formula used:
The formula of the average speed is given by,
${v_{avg}} = \dfrac{{{s_t}}}{t}$
where the average speed is ${v_{avg}}$, the total distance is ${s_t}$ and time taken is $t$ .

Complete step-by-step solution:
At the starting of this trip, the odometer reading was $4200\;km$ .
At the end of the trip, the odometer reading is $4460\;km$ .
The total distance travelled by the motorbike is $\Delta S = 4460 - 4200 = 260km$
The total time taken to cover the distance is $4\;h$ $20\min $
Now conversion of the time from minute to hour is given by dividing the minute value by $60\;$.
Hence, the minute value is:
$\dfrac{{20}}{{60}} = \dfrac{1}{3}h$
Therefore, the total time taken in hours is,
 $4\dfrac{1}{3} = \dfrac{{13}}{3}h$
Now using the average speed formula, we can find the value of speed in terms of $km/h$ as:
${v_{avg}} = \dfrac{{{s_t}}}{t}$
Placing the value of distance and time in the above formula, we get the value of the average speed as:
${v_{avg}} = \dfrac{{260}}{{\left( {\dfrac{{13}}{3}} \right)}}$
$ \Rightarrow {v_{avg}} = \dfrac{{260 \times 3}}{{13}} = 60km/h$
We are asked to calculate the motorbike’s average speed in $m/s$.
To convert kilometers to meters we need to multiply the value in kilometers with $1000\;$ .
We also know that an hour is $60\;$ minutes and $60\;$ minutes is $60 \times 60 = 3600\operatorname{s} $ . Hence to convert hour to the second we need to multiply the value in the hour with $3600\;$ .
Therefore to convert $km/h$ to $m/\operatorname{s} $ we need to multiply $60km/h$ with $\dfrac{{1000}}{{3600}}$ .
i.e. $60km/h = 60 \times \dfrac{{1000}}{{3600}}m/s$
$ \Rightarrow 16.66m/s$
Hence the average speed of the motorbike in $m/s$ is $16.66m/s$ .
As the motorcycle is moving in a straight line without turning back, therefore, the magnitude of average speed and average velocity over a time interval is the same.

Note: Remember that the particle speed is related to distance and particle velocity is related to the displacement that’s why their same value gives the same amount of distance and displacement. For achieving this condition, the particles have to move in a straight line.