Physics, asked by lopadas3140, 9 months ago

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.

Answers

Answered by nirman95
12

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 ]

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