Question

A car braked with a constant deceleration of 8 ft/s2, producing skid marks measuring 100 ft before coming to a stop. how fast was the car traveling when the brakes were first applied?

Answer 1

In physics, it is convenient that there are already derived formulas for rectilinear motion at constant acceleration from Newton's Law of motion. One of these equations useful for this problem is:

2ax = vf2 - v02, where a is the acceleration, x is the distance, vf is the final velocity and v0 is the initial velocity.

Now, a=-8 ft/s2. It is negative because the car is decelerating. The distance x is 100 ft, the vf is equal to 0m/s because the car comes to a stop. The only unknown would be v0.

2(-8 ft/s2)(100 ft) = (0m/s)^2 - v0^2
v0 = 40 m/s