At the scene of an accident, there are skid marks which are 200 feet long showing where a car put on the brakes. The driver swears that he was obeying the speed limit. If we assume that the car braked with a constant deceleration of 16ft/sec^2. We can determine whether or not the driver is telling the truth. Is he? That is, how fast was he going when he applied the brakes (assume the skid marks represent the interval where the brakes were applied)? Please explain your response; note: it is not enough to give an equation and evaluate that equation for the given values. The purpose of this item is to determine where the equation comes from!
To determine whether or not the driver was telling the truth about obeying the speed limit, we need to calculate the initial speed of the car before applying the brakes.
We can use the kinematic equation of motion to solve this problem. The equation we need to use is:
vf^2 = vi^2 + 2ad
Where:
vf = final velocity (which is 0 in this case since the car comes to a stop)
vi = initial velocity (the speed we want to find)
a = acceleration (given as -16 ft/sec^2 because the car is decelerating)
d = distance (given as 200 feet, the length of the skid marks)
Rearranging the equation, we have:
vi^2 = vf^2 - 2ad
Since vf is 0 (the car comes to a stop), the equation becomes:
vi^2 = -2ad
Taking the square root of both sides, we get:
vi = √(-2ad)
Substituting the given values:
vi = √(-2 * (-16 ft/sec^2) * (200 ft))
Simplifying this equation further:
vi = √(6400 ft²/sec²)
Therefore, vi = 80 ft/sec.
So, based on the calculations, the driver was traveling at a speed of 80 ft/sec (approximately 54.5 mph) when they applied the brakes. If the speed limit was lower than this, then the driver was not telling the truth.
V^2 = Vo^2 = 2a*d.
0 = Vo^2 - 32*200,
Vo^2 = 6400, Vo = 80 Ft/s.
Vo = 80FT/s * 1m1/5280Ft. * 3600s/h = 54.5 mi/h. = Initial velocity.