Average velocity of a particle moving in a straight line, with constant accelera

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Average velocity of a particle moving in a straight line, with constant acceleration

a

and initial velocity

u

in first

t

seconds is:

Options:

A . u

B . u+at

C . u+at2

D . u+at2

Answer: Option C
:
C
Given, initial velocity is

u

, acceleration is

a

and total time taken is

t

.
Let

s

be the displacement of the particle.
From second equation of motion,

s = u t + \frac{1}{2} a t^{2}

.

A v e r a g e V e l o c i t y = \frac{T o t a l d i s p l a c e m e n t}{T o t a l t i m e}

∴

A v e r a g e v e l o c i t y = \frac{u t + \frac{{a t}^{2}}{2}}{t}

= u + \frac{a t}{2}

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