You are driving to the grocery store at 18.2 m/s. You are 120.0 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.270 s and that your car brakes with constant acceleration.How far are you from the intersection when you begin to apply the brakes?
To determine the distance you are from the intersection when you begin to apply the brakes, you need to consider your reaction time and the distance traveled during that time. Here's how you can calculate it:
Step 1: Calculate the distance traveled during your reaction time:
Since your reaction time is given as 0.270 s and you're driving at a constant speed of 18.2 m/s, you can use the formula: distance = speed × time.
distance = 18.2 m/s × 0.270 s = 4.914 m.
Step 2: Subtract the distance traveled during your reaction time from the distance to the intersection:
Given that you are 120.0 m from the intersection when the light turns red, you subtract the distance traveled during your reaction time:
distance to the intersection - distance during reaction time = 120.0 m - 4.914 m = 115.086 m.
Therefore, you are approximately 115.086 meters from the intersection when you begin to apply the brakes.