You visited us 1 times! Enjoying our articles? Unlock Full Access!

Finding Average Velocity

A point trave...

Question

A point traversed half of the distance with a velocity $v_{0}$ . The remaining part of the distance was covered with velocity $v_{1}$ for half the time and with velocity $v_{2}$ for the other half of the time. The mean velocity of the point averaged over the whole time of motion

\frac{v_{0} + v_{1} + v_{2}}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 v_{0} + v_{1} + v_{2}}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{v_{0} + 2 v_{1} + 2 v_{2}}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2 v_{0} (v_{1} + v_{2})}{(2 v_{0} + v_{1} + v_{2})}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{2 v_{0} (v_{1} + v_{2})}{(2 v_{0} + v_{1} + v_{2})}$
Let $2 S$ be the total distance travelled
For first half of the journey
$S = v_{0} \times t_{1}$ (where $t_{1}$ is the time taken to complete half of the distance)
For the remaining part of the journey we can say,
$v_{1} t + v_{2} t = S$

$∴ t = \frac{s}{v_{1} + v_{2}}$
Total time = $t_{1} + 2 t$
Mean velocity = $\frac{Total displacement}{Total time}$
$= \frac{2 S}{(\frac{S}{v_{0}}) + 2 (\frac{S}{v_{1} + v_{2}})}$

$= \frac{2}{(\frac{1}{v_{0}}) + (\frac{2}{v_{1} + v_{2}})}$

$= \frac{2 v_{0} (v_{1} + v_{2})}{(2 v_{0} + v_{1} + v_{2})}$

Suggest Corrections

Similar questions

v_{0}

v_{1}

v_{2}

⟨ v ⟩ = \frac{x v_{0} (v_{1} + v_{2})}{2 v_{0} + v_{1} + v_{2}}

x

v_{0}

v_{1}

v_{2}

v_{0}

v_{1}

v_{2}

v_{0}

v_{1}

v_{2}

v_{0}

v_{1}

v_{2}

Join BYJU'S Learning Program