A car leaves skid marks 72m in length. The deceleration is 7.2m/s^2. What is the speed of the car before braking?
V^2 = Vo^2 + 2a*d = 0
Vo^2 = -2a*d = -2*(-7.2)*72 = 1036.8
Vo = 32.2 m/s. = Speed before braking.
To find the speed of the car before braking, we can use the equation of motion:
v² = u² + 2as
where:
v = final velocity (0 m/s since the car comes to a stop)
u = initial velocity (the speed of the car before braking, what we're trying to find)
a = acceleration (-7.2 m/s² since it's deceleration)
s = displacement (72 m, the length of the skid marks)
Rearranging the equation, we have:
u² = v² - 2as
Since the car comes to a stop (v = 0), we can simplify the equation to:
u² = -2as
Plugging in the known values:
u² = -2 * (-7.2 m/s²) * 72 m
Simplifying further:
u² = 1036.8 m²/s²
Now, to find u, we just need to take the square root of both sides of the equation:
u = √(1036.8 m²/s²)
Evaluating the square root:
u ≈ 32.2 m/s
Therefore, the speed of the car before braking was approximately 32.2 m/s.