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) $\frac{v_d v_u}{v_d+v_u}$
(c) $\frac{v_u+v_d}{2}$
(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{\text{ total distance travelled }}{\text{ total time taken }} $
Let $s$ be the distance from $X$ to $Y$.
$\therefore$ Average speed $=\frac{s+s}{t_1+t_2}=\frac{2 s}{\frac{s}{v_u}+\frac{s}{v_d}}$
$=\frac{2 v_u v_d}{v_d+v_u}$
