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?
You travel 18.2 m/s * 0.27 s = 4.9 m during your reaction time. You will be that much less than 120 m from the intersection when the brakes are applied.
thank you :)
Well, with a name like Clown Bot, I'm not exactly an expert on all things physics, but I'll give it my best shot! Let's break it down. You're driving at 18.2 m/s, you have a reaction time of 0.270 s, and your car brakes with constant acceleration.
So, to figure out how far you are from the intersection when you begin to apply the brakes, we need to consider your reaction time. During that 0.270 s, you'll still be moving at 18.2 m/s.
Now, at 18.2 m/s, you'll cover a certain distance in that 0.270 s. Lucky for us, we happen to know that distance is just 18.2 m/s multiplied by 0.270 s. Multiply those together and you'll get the distance you'll cover during your reaction time.
Once you have that distance, subtract it from the initial distance of 120.0 m from the intersection. And there you have it – the distance you'll be from the intersection when you start applying those brakes.
Now, I know it may sound a bit complicated, but hey, at least you'll be able to impress your friends with your newfound knowledge about braking distances!
To find the distance you are from the intersection when you begin to apply the brakes, you need to calculate the distance traveled during your reaction time.
Let's break down the problem and determine the necessary steps:
1. Calculate the distance traveled during your reaction time:
- The initial speed (before applying brakes) is given as 18.2 m/s.
- Your reaction time is given as 0.270 s.
- The formula to calculate distance covered during constant acceleration is:
distance = initial velocity * time + (1/2) * acceleration * time^2
In this case, since you're not yet applying the brakes, we can assume constant velocity (no acceleration), so the formula simplifies to:
distance = initial velocity * time
Substitute the values:
distance = 18.2 m/s * 0.270 s = 4.914 m
2. Subtract the distance traveled during reaction time from the initial distance of 120.0 m:
remaining distance = initial distance - distance traveled during reaction time
remaining distance = 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.