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 how far you are from the intersection when you begin to apply the brakes, you need to calculate the distance your car travels during your reaction time.
Let's break down the problem and use the following variables:
Initial velocity (v0) = 18.2 m/s
Distance to the intersection (s) = 120.0 m
Reaction time (t) = 0.270 s
Final velocity (vf) = 0 m/s (car comes to a stop)
Acceleration (a) = ?
Distance during reaction time (d_reaction) = ?
We can use the following kinematic equation to calculate the distance during the reaction time:
d_reaction = v0 * t
Plugging in the values, we get:
d_reaction = 18.2 m/s * 0.270 s
d_reaction = 4.914 m
Therefore, you are 4.914 meters away from the intersection when you begin to apply the brakes.