Question

A car travels on paths A, B and C within the same time and has velocities ${\text{V}}_{\text{A}}$, ${\text{V}}_{\text{B}}$ and ${\text{V}}_{\text{C}}$ respectively on each path. These paths pass through a group of equally spaced lines. Pick the correct ranking of velocities.

• A. ${\text{V}}_{\text{A}}$ = ${\text{V}}_{\text{B}}$ = ${\text{V}}_{\text{C}}$
• B. ${\text{V}}_{\text{A}}$ > ${\text{V}}_{\text{B}}$ > ${\text{V}}_{\text{C}}$
• C. ${\text{V}}_{\text{A}}$ < ${\text{V}}_{\text{B}}$ < ${\text{V}}_{\text{C}}$
• D. ${\text{V}}_{\text{A}}$ < ${\text{V}}_{\text{B}}$ > ${\text{V}}_{\text{C}}$

Answer 1

The correct option is A ${\text{V}}_{\text{A}}$ = ${\text{V}}_{\text{B}}$ = ${\text{V}}_{\text{C}}$

Three paths A, B and C have been covered with velocities ${\text{V}}_{\text{A}}$, ${\text{V}}_{\text{B}}$, ${\text{V}}_{\text{C}}$

Average velocity= $\frac{\text{Total displacement}}{\text{Total time}}$

Time taken to cover all the paths is the same.
So, Average velocity ∝ Displacement

Displacement for Path A = x
Displacement for Path B = x
Displacement for Path C = x

Since displacement and time is same for all paths, velocities for all paths will also be the same.

$\therefore$ ${\text{V}}_{\text{A}}$ = ${\text{V}}_{\text{B}}$ = ${\text{V}}_{\text{C}}$