Question

When brakes are applied to a moving vehicle, the distance it travels before stopping is called stopping distance. It is an important factor for road safety and depends on the initial velocity ($v_0$) and the braking capacity, or deceleration, -a that is caused by the braking. Derive an expression for stopping distance of a vehicle in terms of $v_0$ and a.

Answer 1

Velocity of moving vehicle$=v_0$ and decceleration $=$a

Final velocity of the vehicale $=0$ (As it stops)

Let the stopping distance be s

Then applying the third equation of motion we have:

$v^2=v_0^2+2(-a)s$

$\Rightarrow 0=v_0^2-2as$

$\Rightarrow s=\frac{v_0^2}{2a}\to$ Expression for stopping distance.