Question

A particle is moving along a straight line with constant acceleration a. Show that the average velocity of the particle during time 0-t is Vavg = ( v+ u)/2. Please don't write irrelevant answers or I don't know.

Answer 1

Given:

Object travels with constant acceleration a. Its initial velocity is u and final velocity is v.

To find:

Average Velocity of object

Concept:

Average velocity is defined as the ratio of total displacement covered by the body to the total time taken.

Calculation:

$v \: avg. = \dfrac{total \: distance}{total \: time}$

$= > v \: avg. = \dfrac{s}{t}$

$= > v \: avg. = \dfrac{ut + \frac{1}{2} a {t}^{2} }{t}$

$= > v \: avg. = u + \frac{1}{2} at$

$= > v \: avg. = u + \dfrac{1}{2} \times ( \dfrac{v - u}{ \cancel t} ) \times \cancel t$

$= > v \: avg. = u + \dfrac{v - u}{2}$

$= > v \: avg. = \dfrac{2u + v - u}{2}$

$= > v \: avg. = \dfrac{u + v }{2}$

[ Hence Proved ]