A car braked at a constant deceleration of 45 ft / s2, producing a skid mark measuring 105 feet before coming to a stop.

How fast was the car travelling when the brakes were first applied?

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To find out how fast the car was traveling when the brakes were first applied, we can use the following equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (0 ft/s, as the car comes to a stop)
u = initial velocity (the speed we're trying to find)
a = acceleration (deceleration in this case, -45 ft/s^2)
s = distance (the length of the skid mark, 105 ft)

Rearranging the equation to solve for u, we have:

u^2 = v^2 - 2as

Substituting the given values, we get:

u^2 = 0^2 - 2(-45)(105)

u^2 = 0 + 9450

u^2 = 9450

Now, we can take the square root of both sides to find u:

u = √9450

u ≈ 97.23 ft/s

Therefore, the car was traveling at approximately 97.23 ft/s when the brakes were first applied.