Question

A particle moves in a straight line with uniform acceleration. Its velocity after time t = 0 is v₁ and at t = t is v₂. The average velocity of the particle in this time interval is $\frac{(v_1+v_2)}{2}$. Is this correct? Substantiate your answer.

Answer 1

A particle moves in a straight line with uniform acceleration. Let us consider a is the acceleration of particle.

initial velocity , u = v₁
velocity of particle after t sec , v = v₂
use formula, v = u + at
then, $v_2=v_1+at$
hence, a = $\frac{v_2-v_1}{t}$

now, use formula, v² = u² + 2as
$v_2^2=v_1^2+2\frac{v_2-v_2}{t}s$
$(v_2-v_1)(v_2+v_1)=2(v_2-v_1)S/t$

$\frac{v_1+v_2}{2}=\frac{s}{t}=\textbf{average velocity}$

hence, it is correct statement.

Answer 2

Answer:

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