Imagine that a car is driving at 50 mph when the light up ahead turns red. The driver slams on the breaks, but it takes him three seconds to come to a complete stop. If we want to know how far the car moved from the time the breaks were applied to when the car was stopped, which kinematics equation do we use?d = vi * t + 1/2 * a(t * t)d = (vi + vf) / 2 * t vf = vi + a * t(vf * vf) = (vi * vi) + 2 * ad

The kinematics equation we would use to determine how far the car moved from the time the brakes were applied to when the car was stopped is:

d = vi * t + 1/2 * a(t * t)

This equation is used when we know the initial velocity (vi), the time (t), and the acceleration (a), and we want to find the distance (d).

In this case, the initial velocity (vi) is 50 mph, the time (t) it takes for the car to stop is 3 seconds, and the acceleration (a) is the change in velocity over time, which is negative because the car is slowing down.

To find the acceleration, we can use the equation:

a = (vf - vi) / t

Where vf is the final velocity, which is 0 because the car comes to a stop.

So, the acceleration (a) is:

a = (0 - 50) / 3 = -16.67 mph per second

Then, we can plug these values into the first equation to find the distance (d):

d = 50 * 3 + 1/2 * -16.67 * (3 * 3) = 150 - 75 = 75 miles

So, the car moved 75 miles from the time the brakes were applied to when the car was stopped.