When brakes are applied to a moving vehicle, the distance it travels before stopping is called stoppingdistance. It is an important factor for road safety and depends on the initial velocity (v0) and thebraking capacity, or deceleration, –a that is caused by the braking. Derive an expression for stoppingdistance of a vehicle in terms of v0 and a

The stopping distance of a vehicle can be derived from the equations of motion.

The equation of motion that relates final velocity (v), initial velocity (v0), acceleration (a), and distance (d) is:

v^2 = v0^2 + 2ad

When the vehicle comes to a stop, the final velocity (v) is 0. So, the equation becomes:

0 = v0^2 + 2ad

We are interested in finding the stopping distance (d), so we rearrange the equation to solve for d:

d = -v0^2 / (2a)

However, since the acceleration is a deceleration (negative acceleration) due to braking, we substitute -a for a:

d = v0^2 / (2(-(-a)))

This simplifies to:

d = v0^2 / (2a)

So, the stopping distance (d) of a vehicle in terms of initial velocity (v0) and deceleration (a) is d = v0^2 / (2a).