A body moves from A to B with a constant speed of 20 m s^-1 and returns from B to A with a con

step 1 Here the body goes from A to B and comes from B to C. This is a scenario. This is point A, point

A body moves from A to B with a constant speed of 20 m...

A body moves from $A$ to $B$ with a constant speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ and returns from $\mathrm{B}$ to $\mathrm{A}$ with a constant speed of $40 \mathrm{~m}$ $\mathrm{s}^{-1}$. The average speed of the body for the whole journey is (a) $(80 / 3) \mathrm{m} \mathrm{s}^{-1}$ (b) $30 \mathrm{~m} \mathrm{~s}^{-1}$ (c) $60 \mathrm{~m} \mathrm{~s}^{-1}$ (d) $40 \mathrm{~m} \mathrm{~s}^{-1}$

A body moves from $A$ to $B$ with a constant speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ and returns from $\mathrm{B}$ to $\mathrm{A}$ with a constant speed of $40 \mathrm{~m}$ $\mathrm{s}^{-1}$. The average speed of the body for the whole journey is
(a) $(80 / 3) \mathrm{m} \mathrm{s}^{-1}$
(b) $30 \mathrm{~m} \mathrm{~s}^{-1}$
(c) $60 \mathrm{~m} \mathrm{~s}^{-1}$
(d) $40 \mathrm{~m} \mathrm{~s}^{-1}$

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Key Concepts

Uniform Motion

Uniform motion refers to the movement of an object at a constant speed, meaning the object covers equal distances in equal intervals of time. This concept simplifies calculations in kinematics as acceleration is absent, allowing the direct use of the relation between distance, speed, and time.

Total Distance and Total Time

The computation of average speed relies on summing up the total distance covered and the total time taken for the journey. Each segment's travel time is determined by dividing its distance by the speed for that segment, and the aggregate time is then used to calculate the overall average speed.

Harmonic Mean in Speed Calculations

When an object covers equal distances at different speeds, the average speed is calculated using the harmonic mean of those speeds. This is because the time taken for each segment is inversely proportional to the speed, making the harmonic mean the appropriate measure rather than the simple arithmetic mean.

Average Speed

Average speed is defined as the total distance traveled divided by the total time taken. It is a crucial concept in kinematics that differs from the arithmetic mean when speeds vary over different segments of a journey.

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