Let's analyze the given options and identify the correct one for average velocity.
The formula for average velocity ([tex]\(V_{av}\)[/tex]) when initial and final velocities are known is given by:
[tex]\[ V_{av} = \frac{u + v}{2} \][/tex]
where
- [tex]\( u \)[/tex] is the initial velocity,
- [tex]\( v \)[/tex] is the final velocity.
Now, let's check each option:
(a) [tex]\( V_{av} = \frac{u + v}{2} \)[/tex]
This directly matches the formula for average velocity. Thus, this option is correct.
(b) [tex]\( V_{av} = \frac{d}{t} \)[/tex]
This represents another way of calculating average velocity, where
- [tex]\( d \)[/tex] is the displacement,
- [tex]\( t \)[/tex] is the total time taken.
While correct, it is a different representation compared to (a) for the given context of using initial and final velocities. Therefore, this option is not provided in the context of the initial and final velocities equation but is a generally valid formula for average velocity.
(c) [tex]\( V_{av} = \frac{d}{t} \)[/tex]
This is the same as option (b), just written differently in the list.
(d) All
Considering that (a) represents the formula using initial and final velocities correctly, and (b) and (c) are valid representations of average velocity in terms of displacement and time, this option suggests that all given formulas are correct representations for calculating average velocity in different contexts.
So, the answer is:
(d) All
