Question

a body moves in a straight line and covers first half the distance with speed 5 metre per second and second half into equal halfs with speed 4 metre per second and 3meter per second respectively the average velocity of the body is

Answer 1

I think when it travelled in 2nd time the time of performing the motion with 3m/s and 4m/s will be equal.

Answer 2

Answer:

The average velocity of the body is 4.12 m/s

Explanation:

Given that,

A body moves in a straight line and covers first half the distance with speed 5 meter per second and second half into equal half with speed 4 meter per second and 3 meter per second respectively.

Let be the total distance 2 x.

Let t be the time taken the first half of the distance

We need calculate the time,

The time is equal to the distance divided by the speed.

$t =\dfrac{d}{v}$

The time for first journey

$t=\dfrac{x}{5}$

Let the other half of the distance be covered in two equal intervals of time t₁

$x = 4t_{1}+3t_{1}=7t_{1}$

The time for second journey

$t_{1}=\dfrac{x}{7}$

The total time will be

$T=t+2t_{1}$

$T=\dfrac{x}{5}+2\times\dfrac{x}{7}$

$T =\dfrac{17x}{35}$

The average velocity is defined as,

$v_{avg}=\dfrac{D}{T}$

Where, D = displacement

T = total time

Put the value of D and T into the formula

$v_{avg}=\dfrac{2x-0}{\dfrac{17x}{35}}$

$v_{avg}=\dfrac{2x\times35}{17x}$

$v_{avg}=\dfrac{2\times35}{17}$

$v_{avg}=4.12\ m/s$

Hence, The average velocity of the body is 4.12 m/s