An object moves with speed v_1, v_2 and v_3 along a line segment A...

An object moves with speed

v_1, v_2

and

v_3

along a line segment

A B, B C

and

C D

respectively as shown in figure. Where

A B=B C

and

A D=3 A B

, then average speed of the object will be:
An object moves with speed v_1, v_2 and v_3 along a line segment A B, B C and C D respectively as shown in figure.

Options

A\frac{v_1 v_2 v_3}{3 $\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}$
B\frac{3 v_1 v_2 v_3}{ $\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}$
C\frac{ $\left(u_1+z_2+v_3\right)}{3}$
D $\frac{\left(v_1+v_2+v_3\right)}{3 v_1 v_2 v_3}$

Correct answer

B. \frac{3 v_1 v_2 v_3}{ $\left(v_1 v_2+v_2 v_3+v_3 v_1\right)}$

Step-by-step solution

Consider,

\mathrm{AB}=x \mathrm{BC}=x 2 x+\mathrm{CD}=3 x \Rightarrow \mathrm{CD}=3 x-2 x=x

Average speed of the object

< \mathrm{v} > =\frac{\text{ Total distance }}{\text{ Total time }} < \mathrm{v}>=\frac{3 x}{\frac{x}{v_1}+\frac{x}{v_2}+\frac{x}{v_3}}=\frac{3 v_1 v_2 v_3}{v_2 v_3+v_1 v_3+v_1 v_2}

Practice Motion in One Dimension on Quantrex Academy →

More from Motion in One Dimension

A particle is moving in a straight line. The variation of position ' x ' as a function of… BITSAT 2024 The distance travelled by a particle starting from rest and moving with an acceleration… BITSAT 2024 A passenger sitting in a train A moving at 90 km /h observes another train B moving in… BITSAT 2023 A balloon is rising vertically up with a velocity of 29 ~ms^ -1 . A stone is dropped from… BITSAT 2021 From a 200 m high tower, one ball is thrown upwards with speed of 10 ms^ -1 and another… BITSAT 2020 Consider the acceleration, velocity and displacement of a tennis ball as its falls to the… BITSAT 2018 A stone is projected with velocity 2 gh , so that it just clears two walls of equal… BITSAT 2018 A ball is dropped vertically from a height d above the ground. It hits the ground and… BITSAT 2018 Full Motion in One Dimension list All BITSAT PYQs