MyQuestionIcon

1

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

Finding Average Velocity

A point trave...

Question

A point traversed half 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. If the mean velocity of the point averaged over the whole time of motion is $⟨ v ⟩ = \frac{x v_{0} (v_{1} + v_{2})}{2 v_{0} + v_{1} + v_{2}}$ . Find $x$ .

Open in App

Solution

Let $s$ be the total distance traversed by the point and $t_{1}$ the time taken to cover half the distance. Further let $2 t$ be the time to cover the rest half of the distance.
Therefore $\frac{s}{2} = v_{0} t_{1}$ or $t_{1} = \frac{s}{2 v_{0}}$ (1)
and $\frac{s}{2} = (v_{1} + v_{2}) t$ or $2 t = \frac{s}{v_{1} + v_{2}}$ (2)
Hence the sought average velocity
$⟨ v ⟩ = \frac{s}{t_{1} + 2 t} = \frac{s}{[\frac{s}{2 v_{0}}] + [\frac{s}{v_{1} + v_{2}}]} = \frac{2 v_{0} (v_{1} + v_{2})}{v_{1} + v_{2} + 2 v_{0}}$

Suggest Corrections

thumbs-up

1

Similar questions

Q. 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 is

Q. 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 one-third of the remaining time and with velocity

v_{2}

for the remaining time. The mean velocity of the point averaged over the whole time of motion

Q. 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

Q. 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

Q. A particle 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 particle averaged over the whole time of motion is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Speed and Velocity

PHYSICS

Watch in App

explore_more_icon

Explore more

Finding Average Velocity

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon