Home
Class 11
PHYSICS
A man traversed half the distance with a...

A man 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 . Find the average speed of the man over the whole time of motion.
.

Text Solution

Verified by Experts

Time to cover the distance `AB`,
`T_(AB)=(s)/(v_(0))` …(i)
Let the time taken to cover the distance `BC` be`t_(BC)`
Given: `(t_(AB))/(2)=(s_(1))/(v_(1))` …(ii)
`S_(1)`= dismilarly, covered during first halt of time
From (ii) and (iv), `s_(1)=v_(2) (t_(AB))/(2)` ..(iii)
Similarly, `s_(2)=v_(2)(T_(AB))/(2)` ...(iv)
From (iii) and (iv),
`s_(1)+s_(2)=s=(v_(1)+v_(2))/(2) t_(BC)`
Hence, `t_(BC)=(2s)/(v_(1)+v_(2))`
Hence, average velocity `v_(AC)=(2s)/(t_(AB)+t_(BC))`
`v_(AC)=(2s)/((s)/(v_(0))+(2s)/((v_(1)+v_(2)))) rArr v_(AC)=(2v_(0)(v_(1)+v_(2)))/((v_(1)+v_(2)+2v_(0)))`.
Promotional Banner

Topper's Solved these Questions

  • KINEMATICS-1

    CENGAGE PHYSICS|Exercise Solved Examples|9 Videos

  • KINEMATICS-1

    CENGAGE PHYSICS|Exercise Exercise 4.1|17 Videos

  • GRAVITATION

    CENGAGE PHYSICS|Exercise INTEGER_TYPE|1 Videos

  • KINEMATICS-2

    CENGAGE PHYSICS|Exercise Exercise Integer|9 Videos

Similar Questions

Explore conceptually related problems

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. Find the mean velocity of the point averaged over the whole time of motion.

A cae is travelling along a straight line. It covers one-half of the total, distance with a velocity 10 km//h . The remaining part of the distance was covered with velocity 12 ms^(-1) . For half the time and with velocity 16 ms^(-1) for the other half the tiem. Find the average speed over the whole time of motion.

A body travelling along a straight line traversed one-third of the total distance with a velocity v_1 . The remaining part of the distance was covered with a velocity v_2 for half the time and with velocity v_3 for the other half of time. The mean velocity averaged over the whole time of motion

A particle travels along a straight line. It covers halg the distance with a speed (v). The remaining part of the distance was covere with speed v_(1) for half the time and with speed v_(2) for the other half the time . Find the average speed of the particle over the entire motion.

A point traversed half of the total distance covered by its with velocity v_0 .The remaining part of the distance was covered with velocity v_1 for half of the remaining time, and with velocity v_2 for the other half of the remaining time.Find the mean velocity of the point over the whole time of motion.

A body travelling along a straight line traversed one third of the total distance with a velocity 4m/s. The remaining part of the distance was covered with a velocity 1 m/s for half the time and with velocity 3 m/s for the other half of time. The mean velocity averaged over the whole time of motion is :

A body travelling along a straight line traversed one thired of the total distance with a velocity 4 ms^(-10 . The remaining part of the distance was covered with a velocity 2 ms^(-1) for half the time and with velocity 6 ms^(-1) for the other hald of time . What is the mean velocity averaged over te whle time of motin ?

A particle traversed on third 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 a velocity v_(2) for the remaining half of time. Assuming motion to be rectilinear, find the the mean velocity of the particle averaged over the whole time of motion.

09A body moving in a straight line covers half the distance with a speed V the remaining part of the distance was covered with a speed V for half the time and with a speed V for the other half of the time.What is the average speed of the body?

A particle is moving in a straight line. It covers half of the total distance with velocity v_(0) Remaining half distance is covered with a velocity v_(1) for half the time and with velocity v_(2) for another half of time. Find the average velocity of the particle.