SATHEE: Motion in a Straight Line

Motion in a Straight Line - Result Question 4

4. 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 [2007]

(a) $\sqrt{v_{u} v_{d}}$

(b) $\frac{v_{d} v_{u}}{v_{d} + v_{u}}$

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

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Answer:

Correct Answer: 4. (d)

Solution:

(d) Average speed

$= \frac{total distance travelled}{total time taken}$

Let $s$ be the distance from $X$ to $Y$ .

$∴$ Average speed $= \frac{s + s}{t_{1} + t_{2}} = \frac{2 s}{\frac{s}{v_{u}} + \frac{s}{v_{d}}}$

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

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Motion in a Straight Line - Result Question 4

4. A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is [2007]

Answer:

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4. 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 [2007]