Explanation :
When a person is sliding with constant velocity, the forces that are acting on him are :
(1) Weight, W = mg where g is acceleration due to gravity.
(2) Friction forces acting opposite to the direction of motion.
(3) Normal force.
The forces acting on the person is balanced because the person is sliding with constant velocity.
From figure it is clear that, friction force is balanced by and normal is balanced by
.
The braking distance is the distance traveled by a car experiencing a braking force until it comes to rest.
Our initial energy is solely kinetic:
And, since the car goes to rest, it is no longer in motion. It will have no kinetic energy.
Therefore, there was work done by the braking force.
Recall the definition of work:
Or in this case, since the displacement and breaking force are antiparallel:
This is equivalent to the dissipation of kinetic energy:
Now, to visualize this, let's rearrange the equation to solve for displacement.
<u>There is a direct, SQUARE relationship between necessary braking distance speed. </u>
If the speed was reduced by 10.3 percent, its new speed is only 89.7% percent of the original, so:
The reduction by a percentage is: