First slide

Rectilinear Motion

Question

A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the
body for the total time of flight are

Moderate

A

$\vec{v} / 2 and v / 2$
B

$0 and v / 2$
C

$0 and 0$
D

$\vec{v} / 2 and 0$

Solution

Average velocity = 0 because net displacement of the body is zero.
$Average speed = \frac{Total distance covered}{Time of flight} = \frac{2 H_{max}}{2 u / g}$
$\Rightarrow v_{a v} = \frac{2 u^{2} / 2 g}{2 u / g} \Rightarrow v_{a v} = u / 2$
Velocity of projection = v (given)
$∴ v_{a v} = v / 2$

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