Average Speed Calculation: Distance, Time, and Velocity

Question:

A car travels the first half of a distance between two places at a speed of 30 Kmh^-1 and the second half of the distance at 50 Kmh^-1.What is the average speed of the car for the whole journey?

Solution:

Average speed of the car:

ALITER:

Average speed of the car $${=\frac{2v_1v_2}{v_1+v_2}}$$

Speed of the car at the first half distance (v₁)= 30Kmh^-1

Speed of the car during the remaining half distance (v₂) =50 Kmh^-1

$${Average \ speed=\frac{Total \ distance}{Total \ time \ taken}}$$

$${Average \ speed=\frac{2d}{\frac{d}{v_1}+\frac{d}{v_2}}}$$

$${Average \ speed =\frac {2d}{d(\frac{1}{v_1}+\frac{1}{v_2)}}}$$

$${Average \ speed= \frac{2v_1v_2}{v_1+v_2}}$$

$${Average \ speed=\frac{2(30)(50)}{30+50}}$$

$${Average \ speed=\frac {3000}{80}}$$

$${Average \ speed =37.5 \ \frac{Km}{h}}$$

Links to this blogpost

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Average Speed Calculation: 3/4th and 1/4th Distance

Average Speed of a Car Traveling at Varying Speeds | Calculation & Concept