Question

A point traversed half distance with a velocity V₀. The remaining part of the distance was covered with velocity V₁ for half of time and velocity V₂ for other half of time. Find average velocity over whole time of motion.​

Answer 1

In this kind of questions , we can follow this rule :

In the 2nd half of journey , the point covered half of time with velocity v1 and rest half time with velocity v2.

So for that 2nd half journey , the average Velocity will be $v_{net}$.

$v_{net} = \dfrac{v1 + v2}{2}$

Now we can say that the particle travelled 1st half distance with velocity $v_{0}$ and the 2nd half distance with $v_{net}$.

So final average velocity be avg. v

$avg. \: v = \dfrac{2(v_{0})(v_{net})}{(v_{0} +v_{net}) }$

$= > avg. \: v = \dfrac{2(v_{0})( \frac{v1 + v2}{2} )}{(v_{0} + \frac{v1 + v2}{2} ) }$

$= > avg. \: v = \dfrac{2(v_{0})( \frac{v1 + v2}{ \cancel2} )}{( \frac{2v_{0} + v1 + v2}{ \cancel2} ) }$

$= > avg. \: v = \dfrac{2(v_{0})( v1 + v2)}{( 2v_{0} + v1 + v2) }$

So final answer :

$\boxed{ \red{ \huge{ \bold{avg. \: v = \dfrac{2(v_{0})( v1 + v2)}{( 2v_{0} + v1 + v2) } }}}}$

Answer 2

Answer:

A point traversed half the distance with a velocity v0. The remaining part of the distance was covered with velocity v1 for half the time, and with velocity v2 for the other half of the time. If the mean velocity of the point averaged over the whole time of motion is ⟨v⟩=2v0+v1+v2xv0(v1+v2).