The initial velocity of a particle is u (at t=0) and the acceleration f is given by $f = a t$ where $a$ is a constant. Which of the following relation is valid?

Q. If

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

, where

S

is displacement,

u

is initial velocity (constant),

a

is acceleration (constant) and

t

is time taken, then differentiation of

S

w.r.t.

t

will be

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The average velocity of a particle moving in a straight line, with constant acceleration, ′a′ and initial velocity, ′u′ in the first ′t′ seconds is:

The correct option is C u+at2 Average Velocity =Total displacementTotal time =ut+at22t [∵ Displacement, s=ut+12at2] =u+at2

The average velocity of a particle moving in a straight line, with constant acceleration, $^{'} a^{'}$ and initial velocity, $^{'} u^{'}$ in the first $^{'} t^{'}$ seconds is:

The correct option is C
$u + \frac{a t}{2}$

Average Velocity $= \frac{Total displacement}{Total time}$
$= \frac{u t + \frac{{a t}^{2}}{2}}{t}$
[ $∵$ Displacement, $s = u t + \frac{1}{2} a t^{2}$ ]
$= u + \frac{a t}{2}$