Question

A car is travelling at constant velocity. Its brakes are then applied, causing uniform deceleration. Which graph shows the variation with distance s of the velocity v of the car?

I want an answer ASAP and with explanation

Answer 1

First, note that all these graphs are velocity vs distance graphs.
Therefore, you need to find a relation that explains how velocity changes with distance.

In a uniformly decelerated motion we have:
s = v₀·t - 1/2·a·t²
v = v₀ - a·t

Solve the first equation for t:
t = [v₀ +/- √(v₀²-2·a·s)] / a
For our purpose what is most important is the dependace:
t ∝ √-s

Now, substitute in the second equation, and we get:
v ∝ √-s

Hence, the graph representing a radical function of a negative value is A).