You are driving to the grocery store at 14.8 m/s. You are 140.0 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.440 s and that your car brakes with constant acceleration. You are 133 m from the intersection when you begin to apply the brakes.
a) What acceleration will bring you to rest as you just reach the intersection?
b) How long does it take you to stop?
see other post.
To solve this problem, we can use the basic equations of motion for constant acceleration.
a) The first step is to find the initial velocity (vi) of the car when you start applying the brakes. We can use the equation:
vi = vf + at
where vi is the initial velocity, vf is the final velocity (which is 0 m/s since we are trying to bring the car to a stop), a is the acceleration, and t is the time.
We know that vf = 0 m/s and t = 0.440 s (the reaction time). Rearranging the equation, we get:
vi = 0 + a(0.440)
Since we are given the initial velocity vi as 14.8 m/s, we can substitute that value into the equation to find the acceleration:
14.8 = a(0.440)
Now, we can solve for the acceleration (a):
a = 14.8 / 0.440
a ≈ 33.638 m/s²
Therefore, the acceleration that will bring you to rest as you just reach the intersection is approximately 33.638 m/s².
b) To find the time it takes to stop, we can use the equation:
vf = vi + at
where t is the time, vf is the final velocity (0 m/s), vi is the initial velocity (14.8 m/s), and a is the acceleration (-33.638 m/s²).
Substituting the given values, we have:
0 = 14.8 + (-33.638)t
Rearranging the equation, we get:
33.638t = 14.8
t = 14.8 / 33.638
t ≈ 0.439 s
Therefore, it takes approximately 0.439 seconds for you to stop.