Question

A car travels 1/3 of the distance on a straight road with a velocity of 10 kmph
next one-third with a velocity 20 kmph and the last one-third with a velocity
of 60 kmph. The average velocity of the car for the entire journey is​

Answer 1

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Answer 2

Solution :

⏭ Given:

✏ A car travels first 1/3 of the total distance with velocity 10kmph, second 1/3 of the toal distance with velocity 20kmph and last 1/3 of the total distance with velocity 60kmph.

⏭ To Find:

✏ The average velocity of car during the whole journey.

⏭ Formula:

✏ Let body covers first 1/3 distance with velocity V1, second 1/3 distance with velocity V2 and last 1/3 distance with velocity V3 then average velocity of the body is given by

$\bigstar \: \underline{ \boxed{ \bold{ \sf{ \pink{V_{av} = \frac{3V_1V_2V_3}{V_1V_2 + V_2V_3 + V_1V_3}}}}}} \: \bigstar$

⏭ Calculation:

$\implies \sf \: V_{av} = \dfrac{3 \times 10 \times 20 \times 60}{(10 \times 20) + (20 \times 60) + (60 \times 10)} \\ \\ \implies \sf \: V_{av} = \dfrac{36000}{200 + 1200 + 600} \\ \\ \implies \sf \: V_{av} = \dfrac{36 \cancel{ \blue{000}}}{2 \cancel{ \red{000}}} \\ \\ \implies \underline{ \boxed{ \bold{ \sf{ \orange{ \large{V_{av} = 18 \: kmph}}}}}} \: \gray{ \bigstar}$

⏭ Additional information:

• Velocity is vector quantity.
• Vector quantity has both magnitude as well as direction.
• Average velocity is defined as ratio of total distance(displacement) to the total time.