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 between your car and the intersection when you begin to apply the brakes, we can use the kinematic equation:
distance = initial distance + velocity * time + (1/2) * acceleration * time^2
Given:
Initial velocity (v0) = 18.2 m/s
Initial distance (d0) = 120.0 m
Reaction time (t) = 0.270 s
Since you are driving at a constant velocity, the equation simplifies to:
distance = initial distance + velocity * reaction time
Substituting the given values:
distance = 120.0 m + 18.2 m/s * 0.270 s
Simplifying:
distance = 120.0 m + 4.914 m
Therefore, when you begin to apply the brakes, you are approximately 124.914 meters from the intersection.