You are driving to the grocery store at 20 m/s. You are 110 m from an intersection when the traffic light turns red. Assume that your reaction time is 0.70 s and that your car brakes with constant acceleration.How far are you from the intersection when you begin to apply the brakes?
d = 110 - Vo*t = 110 - 20*0.7 = 96 m.
To find the distance you are from the intersection when you begin to apply the brakes, we can use the equation of motion.
The equation of motion for the initial velocity (u), final velocity (v), acceleration (a), and distance (s) is:
v^2 = u^2 + 2as
We are given:
- Initial velocity (u) = 20 m/s
- Final velocity (v) = 0 m/s (because you need to stop at the intersection)
- Acceleration (a) = ? (to be determined)
- Distance (s) = 110 m
Using the equation of motion, we can rearrange it to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
a = (0^2 - 20^2) / (2 * 110)
a = -20^2 / 220
a = -2 m/s^2
The negative sign indicates that the acceleration is opposing the direction of motion (deceleration).
Now, we can determine the time it takes to apply the brakes. We are given that the reaction time is 0.70 s, so the total time it takes to apply the brakes is equal to this reaction time.
Next, we use the equation of motion to find the distance traveled during the reaction time:
s = ut + (1/2)at^2
where:
- Initial velocity (u) = 20 m/s
- Time (t) = 0.70 s
- Acceleration (a) = -2 m/s^2
Substituting the values into the equation:
s = (20 * 0.70) + (1/2)(-2)(0.70)^2
s = 14 + (-0.49)
s = 13.51 m
Therefore, when you begin to apply the brakes, you are approximately 13.51 meters away from the intersection.