Deceleration, velocity, acceleration, distance

[munchy35]

1.

You are driving toward a traffic signal when it turns yellow. Your speed is the legal speed limit of v0=55 km/h.: your best deceleration rate has the magnitude a = 5.18 m/s^2. Your best reaction time to begin braking is T = .75S. To avoid having the front of your car enter the intersection after the light turns red, should you brake to a stop or continue to move at 55 km/h if the distance to the intersection and the duration of the yellow light are a) 40 m and 2.8 s, and b) 32 m and 1.8s? Give an answer of brake, continue, either (if either strategy works) or neither (if neither strategy works and the yellow duration is inappropriate).

2.
x = x0 + v0 t + .5at^2

any derivatives needed...dx/dt? dv/dt?


3.

well the first thing i tried was converting the 55 km/h to the correct units of m/s. so 55 km/h = roughly about 15.277778 m/s.

then i drew some pictures and realized i need to use a formula involving v0, time, distance, and acceleration. I'm just confused on how to use T=.75 s. I'm getting a physics tutor soon, but since i don't have one yet...i need a lot of help. i just don't even know where to begin.

 

[semc]

I believe you can use the reaction time to calculate the distance you travel before applying the brake. You should be able to find the answer if you just use the equation you have quoted I don't think derivatives are required.

 

[tomcue]

1. To determine whether you should brake to a stop or continue at 55 km/h, we need to use the formula x = x0 + v0t + 1/2at^2, where x is the distance, x0 is the initial distance, v0 is the initial velocity, t is time, and a is acceleration. We also need to consider the reaction time, T, which is the time it takes for you to start braking after seeing the yellow light.

For situation a) where the distance to the intersection is 40 m and the yellow light duration is 2.8 s, we can plug in the values into the formula: 40 = 0 + (15.277778)(2.8) + 1/2(5.18)(2.8)^2. This gives us a final distance of 40.092 m, which means you should continue at 55 km/h to safely pass through the intersection before the light turns red.

For situation b) where the distance to the intersection is 32 m and the yellow light duration is 1.8 s, we can plug in the values into the formula: 32 = 0 + (15.277778)(1.8) + 1/2(5.18)(1.8)^2. This gives us a final distance of 32.036 m, which means you should brake to a stop to avoid entering the intersection after the light turns red.

2. The derivatives needed for this problem are dx/dt and dv/dt, which represent the instantaneous velocity and acceleration, respectively. To find dx/dt, we simply take the derivative of the position equation: dx/dt = v0 + at. And to find dv/dt, we take the derivative of the velocity equation: dv/dt = a.

3. It's great that you have a physics tutor coming soon, as this problem involves some important concepts in physics such as acceleration, velocity, and distance. It's important to understand how to use the formulas and equations in order to solve problems like this one. In addition, understanding the concept of reaction time and how it affects your decision-making while driving is crucial for safe driving. Keep practicing and asking questions, and your understanding of this topic will improve.