First slide

Average Speed

Question

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

Moderate

A

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

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

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

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

Solution

we define
Average speed = $\frac{Distance travelled}{Time taken} = \frac{d}{T}$
$Let t_{1} and t_{2} be times taken by the car to go from X to Y and then from Y to X respectively$
Then, $t_{1} + t_{2} = [\frac{XY}{v_{u}}] + [\frac{XY}{v_{d}}] = XY (\frac{v_{u} + v_{d}}{v_{u} v_{d}})$
Total distance travelled d = XY +XY = 2XY
Therefore, average speed of the car for this round trip is
$v_{av} = \frac{2 XY}{XY (\frac{v_{u} + v_{d}}{v_{u} v_{d}})} or v_{av} = \frac{2 v_{u} v_{d}}{v_{u} + v_{d}}$

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