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A car moving on a straight road covers one third of a certain distance with 20 Km/h and the rest with 60 Km/h. The average speed is:

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: This could be simply solved by breaking the total distance into three parts and applying the basic formula of mean speed. The average speed is the distance per time ratio.
Formula used: Here, we will use the basic formula of speed, distance and time:
${{\text{V}}_{{\text{avg}}}}{\text{ = }}\dfrac{{\text{D}}}{{\text{T}}}$
Here, ${{\text{V}}_{{\text{avg}}}}$ is the mean speed of the car
${\text{D}}$ is the total distance travel
$T$ is the travel time

Complete step by step answer:
We will start by considering the total distance to be ${\text{d}}$,
For the first third of the distance:
${{\text{v}}_{\text{1}}}{\text{ = 20kmph}}$
${{\text{t}}_{\text{1}}}{\text{ = }}\dfrac{{{\text{d/3}}}}{{{{\text{v}}_{\text{1}}}}}$
Time taken to cover one third distance = $\dfrac{{d/3}}{{{v_1}}} = \dfrac{{d/3}}{{20}}$
Similarly, for the second third of the distance:
${{\text{v}}_{\text{2}}}{\text{ = 60kmph}}$
${{\text{t}}_{\text{2}}}{\text{ = }}\dfrac{{{\text{2d/3}}}}{{{{\text{v}}_{\text{2}}}}}$
Now the mean speed over distance:
${{\text{v}}_{{\text{avg}}}}{\text{ = }}\dfrac{d}{{\dfrac{{d/3}}{{20}} + \dfrac{{2d/3}}{{60}}}} = 36 km/hr$
Thus, the mean speed over the entire distance is 36kmph.

Additional Information: Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. The average speed of an object tells you on an average rate at which it will cover the distance that an object has a speed of 30km/hour, its position will change on an average by 30km each hour. Average speed is a rate that is a quantity divided by time taken to get that quantity.
The first scientist to measure speed as distance over time was Galileo.

Note: It should always be kept in mind that there is a difference between speed and velocity. Just as distance and displacement have distinctly different meanings, same is the situation between speed and velocity. Velocity is a vector quantity that refers to the rate at which an object changes its position whereas speed is a scalar quantity that refers to how fast an object is moving. Velocity gives us a sense of direction whereas speed does not give any sense of direction.
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