How fast was a car driving when it applied its brakes after striking someone who remained on the hood, and did notcome to a stop for 153 feet, while descending a hill?
To determine the initial speed of the car, we can use the equation of motion for an object under constant acceleration. In this case, the car is decelerating due to the application of its brakes. The equation is:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s since the car comes to a stop)
u = initial velocity (what we want to find)
a = acceleration (assumed to be constant)
s = displacement (153 feet or 46.63 meters)
Rearranging the equation, we have:
u^2 = v^2 - 2as
Substituting the values:
u^2 = 0^2 - 2 * a * 46.63
Since the car comes to a stop, its final velocity is 0 m/s. The acceleration (a) can be calculated using another equation:
a = Δv / Δt
As we don't have the time taken to stop, we can't calculate the acceleration directly. However, we know that the car stopped after a displacement of 153 feet, so we will assume that the car's deceleration is constant throughout.
Now, we need to convert the distance from feet to meters:
s = 46.63 m
Let's assume the acceleration remains constant and solve the equation for the initial velocity (u):
u^2 = 0^2 - 2 * a * 46.63
Simplifying further:
u^2 = -92.26a
To calculate the initial speed of the car, we need to know the acceleration of the car during braking. If you have that value, you can substitute it in the equation and solve for u. Keep in mind that the actual value may vary depending on the car's braking system, road conditions, and other factors.