First slide

Average Speed

Question

A car moves from X to Y with a uniform speed $v_{u}$ and returns to X with a uniform speed $v_{d}$ . The average speed for this round trip is

Moderate

A

$\sqrt{v_{u} v_{d}}$
B

$\frac{v_{d} v_{u}}{v_{d} + v_{u}}$
C

$\frac{v_{u} + v_{d}}{2}$
D

$\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}$

Solution

Average speed= $\frac{t o t a l d i s \tan c e t r a v e l l e d}{t o t a l t i m e t a k e n}$
$= \frac{s + s}{t_{1} + t_{2}} = \frac{2 s}{\frac{s}{v_{u}} + \frac{s}{v_{d}}} = \frac{2 v_{u} v_{d}}{v_{d} + v_{u}}$

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