For a particle undergoing rectilinear motion with uniform acceleration, the magnitude of displacement is one third the dis†an ce covered in some time interval. The magnitude of final velocity is less than magnitude of initial velocity for this time interval. Then the ratio of initial speed to the final speed for this time interval is : (A) V2 (B) 2 (C) 73 (D) 3

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Q. Statement - 1 : For a particle undergoing rectilinear motion with constant acceleration, the average velocity cannot be equal for two different time intervals.
Statement -2 : The average velocity of particle moving with constant acceleration in a time interval is

\frac{\to u + \to v}{2}

,
where

\to u

is the initial velocity and

\to v

is the final velocity.

Explain clearly, with examples, the distinction between:
a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;
b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.
When is the equality sign true? [For simplicity, consider one-dimensional motion only].

Q. For a body moving with uniform acceleration

a

, initial and final velocities in a time interval

t

are

u

and

v

respectively. Then, its average velocity in the time interval

t

is :

Q. Statement - 1 : In a given time interval, the average speed of a particle may be equal to magnitude of average velocity.
Statement - 2 : The magnitude of instantaneous velocity is equal to instantaneous speed of a particle in motion.

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