In coming to a stop, a car leaves skid marks 77 long on the highway Assuming a deceleration of 7.20 , estimate the speed of the car just before braking
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To estimate the speed of the car just before braking, we can use the equation of motion relating distance, initial velocity, final velocity, and acceleration:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity
a = acceleration
s = distance
Given the information:
s = 77 ft
a = -7.20 ft/s^2 (negative sign indicates deceleration)
We need to solve for u (initial velocity).
Rearranging the equation, we have:
u^2 = v^2 - 2as
Since the car comes to a stop, the final velocity (v) is 0. Substituting these values into the equation, we get:
u^2 = 0 - 2(-7.20)(77)
u^2 = 1103.20
Taking the square root of both sides, we find:
u = √1103.20
Calculating the square root, we get:
u ≈ 33.20 ft/s
Therefore, the estimated speed of the car just before braking is approximately 33.20 feet per second.