Kinematics Question 347
Question: A point traversed half of the distance with a velocity $ v _{0} $ . The half of remaining part of the distance was covered with velocity $ v _{1} $ and second half of remaining part by $ v _{2} $ velocity. The mean velocity of the point, averaged over the whole time of motion is
Options:
A) $ \frac{{{v} _{0}}\text{+}{{v} _{1}}+{{v} _{2}}}{3} $
B) $ \frac{2{{v} _{0}}\text{+}{{v} _{1}}+{{v} _{2}}}{3} $
C) $ \frac{{{v} _{0}}\text{+.2}{{v} _{1}}+2{{v} _{2}}}{3} $
D) $ \frac{{{v} _{0}}\text{+2(}{{v} _{1}}+{{v} _{2}})}{\text{(2}{{v} _{0}}\text{+}{{v} _{1}}+{{v} _{2}})} $
Show Answer
Answer:
Correct Answer: D
Solution:
Let the total distance be d. Then for first half distance, time $ =\frac{d}{2{{v} _{0}}} $ ,
next distance. = $ v _{1}t $ and last half distance = $ v _{2}t $
$ v _{1}t+v _{2}t$=$\frac{d}{2}\text{ t=}\frac{d}{2(v _{1}+v _{2})} $
Now average speed $ t=\frac{d}{\frac{d}{2v _{0}}+\frac{d}{2(v _{1}+v _{2})}+\frac{d}{2( v _{1}+v _{2} )}} $
= $ \frac{2{{v} _{0}}( v{ _{1}}\text{+}{{v} _{2}} )}{( v _{{1}}\text{+}{{v} _{2}} )\text{+2}{{v} _{0}}} $
