Given:
90m skid mark
.50 coefficient of friction between the tires and skid mark
How fast is the car moving when the brakes initially applied?
To determine the initial speed of the car when the brakes were applied, we can use the equation of motion that relates the skid distance, coefficient of friction, and initial speed of the car.
The equation we will use is:
v^2 = u^2 + 2as
Where:
v = final velocity (which is 0 as the car stops)
u = initial velocity (what we are trying to find)
a = acceleration (negative, since the car is decelerating due to braking)
s = skid distance
First, let's rearrange the equation:
u^2 = v^2 - 2as
Since the final velocity (v) is 0 when the car comes to a stop, the equation simplifies further to:
u^2 = -2as
Now, let's substitute the given values:
s = 90m
a = -0.50 (negative because it's deceleration due to braking)
Plugging these values into the equation:
u^2 = -2 * (-0.50) * 90m
u^2 = 180m
Taking the square root of both sides to solve for u:
u = √(180m)
u ≈ 13.42m/s
Therefore, the initial speed of the car when the brakes were applied is approximately 13.42 m/s.
To find the initial speed of the car when the brakes are first applied, we can use the formula for calculating deceleration:
Acceleration (a) = (Coefficient of friction) × (Gravity)
Rearranging the formula, we can solve for the initial speed (v):
Initial speed (v) = √((2 × Acceleration × Skid mark length))
First, let's calculate the acceleration:
Acceleration (a) = (0.50) × (9.8 m/s^2) [assuming acceleration due to gravity is approximately 9.8 m/s^2]
Acceleration (a) = 4.9 m/s^2
Now, let's substitute the values into the formula to find the initial speed:
Initial speed (v) = √((2 × 4.9 m/s^2 × 90 m))
Initial speed (v) = √(882 m^2/s^2)
Initial speed (v) = 29.7 m/s
Therefore, the car is initially moving at approximately 29.7 meters per second when the brakes are applied.