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 calculate the distance from the intersection when you begin to apply the brakes, we need to find the distance traveled during your reaction time.
Given:
Initial speed (vi) = 18.2 m/s
Distance to the intersection (d) = 120.0 m
Reaction time (t) = 0.270 s
First, we'll calculate the distance traveled during the reaction time using the formula: distance = speed × time.
Distance during reaction time = vi × t
Distance during reaction time = 18.2 m/s × 0.270 s
Distance during reaction time = 4.914 m
Now, subtract the distance traveled during the reaction time from the total distance to find the remaining distance to the intersection when you begin to apply the brakes.
Remaining distance = d - Distance during reaction time
Remaining distance = 120.0 m - 4.914 m
Remaining distance = 115.086 m
Therefore, you are approximately 115.086 meters from the intersection when you begin to apply the brakes.