Motion in a Straight Line - Result Question 3
3. A particle covers half of its total distance with speed $v_1$ and the rest half distance with speed $v_2$. Its average speed during the complete journey is
[2011M]
(a) $\frac{v_1 v_2}{v_1+v_2}$
(b) $\frac{2 v_1 v_2}{v_1+v_2}$
(c) $\frac{2 v_1^{2} v_2^{2}}{v_1^{2}+v_2^{2}}$
(d) $\frac{v_1+v_2}{2}$
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Answer:
Correct Answer: 3. (b)
Solution:
- (b) Let the total distance covered by the particle be $2 s$. Then
$v _{a v}=\frac{2 s}{\frac{s}{v_1}+\frac{s}{v_2}}=\frac{2 v_1 v_2}{v_1+v_2}$
The average speed of an object is the total distance travelled by the object divides by the elapsed time to cover that distance. It’s a scalar quantity which means it is defined only by magnitude. A related concept, average velocity, is a vector quantity. A vector quantity is defined by magnitude and direction both.
