Solving AP Mechanics Problem: Find DeltaTy for Vo & Minimal Time Interval

In summary, the problem is asking for the required time interval that the traffic light should stay yellow in order for a car traveling at a constant speed Vo to be able to safely pass through the intersection without speeding up. The solution involves finding the stopping distance and time, and the coasting time from the distance at which the car could stop before the intersection. The minimum of these two times will determine the minimum time interval that the light should stay yellow. The pattern of variation of this time interval with Vo is physically accounted for by the velocity of the car and its braking ability. The minimum time interval occurs at a value of Vo that allows the car to reach the other side of the intersection without speeding up or stopping.
  • #1
fantolay
5
0

Homework Statement


Assume you are driving at the speed limit Vo. As you approach an intersection 22m wide, you see the light turn yellow. During your reaction time of .6s, you travel at a constant speed as you recognize the warning, decide whether to stop or to go through the intersection, and move your foot to the brake if you must stop. Your car has good brakes and can accelerate at -2.4m/s2. Before it turns red, the light should stay yellow long enough for you to be able to get to the other side of the intersection without speeding up, if you are too close to the intersection to stop before entering it. (Suggestion: You may find it easier to do part (a) after part (b).)

a) Find the required time interval DeltaTy that the light should stay yellow in terms of Vo.
Evaluate answer for...
b) Vo = 8m/s
c) Vo = 11m/s
d) Vo = 18m/s
e) Vo = 25m/s

Evaluate your answer for...
f) Vo approaching zero
g) Vo approaching infinity
h) Describe pattern of variation of DeltaTy with Vo. Account for answers to parts (f) and (g) physically.
i) For waht value of Vo would Deltaty be minimal?
j) What is the minimum time interval for part (i)?

Homework Equations


Probably the big 4 will be necessary in some form or another.

The Attempt at a Solution


I have no idea where to begin with this problem. I really don't even understand what it is asking and what is going on in the scenario.

I really appreciate any help.
Thanks guys.
 
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  • #2
Start with part (b) as suggested. Find the stopping distance and time. Find the time to coast through the intersection from the distance from which you could stop. The light must stay yellow for the minimum of these two times.
 
  • #3

Thank you for your question. I can help you understand and solve this AP Mechanics problem.

Firstly, let's break down the problem into smaller parts to make it easier to understand. You are driving at a constant speed, Vo, and approaching an intersection that is 22m wide. When you see the light turn yellow, you have a reaction time of 0.6 seconds to decide whether to stop or go through the intersection. Your car has good brakes and can accelerate at -2.4m/s2. The light should remain yellow long enough for you to pass through the intersection without speeding up, if you are too close to stop before entering it.

Now, let's tackle part (a) of the problem. We need to find the required time interval, DeltaTy, in terms of Vo. This means we need to find an equation that relates Vo and DeltaTy. To do this, we can use the kinematic equations, specifically the one that relates displacement, velocity, acceleration, and time:

d = vit + 1/2at^2

where d is the displacement, vi is the initial velocity, a is the acceleration, and t is the time.

In this case, our displacement is 22m (the width of the intersection), our initial velocity is Vo, and our acceleration is -2.4m/s^2 (since we are slowing down). We also have a reaction time of 0.6 seconds, so our total time will be DeltaTy + 0.6 seconds.

Putting these values into the equation, we get:

22 = Vo(DeltaTy + 0.6) + 1/2(-2.4)(DeltaTy + 0.6)^2

Now, we can simplify this equation and solve for DeltaTy in terms of Vo. I will leave this part for you to try.

Once you have that equation, you can use it to solve parts (b)-(e) by plugging in the given values for Vo.

Moving on to part (f), when Vo approaches zero, our equation for DeltaTy simplifies to:

22 = 0.6^2

This means that the minimum time interval for the light to stay yellow is 0.6 seconds, regardless of your initial velocity.

For part (g), when Vo approaches infinity, our equation for DeltaTy simplifies to:

22 =
 

Related to Solving AP Mechanics Problem: Find DeltaTy for Vo & Minimal Time Interval

What is the formula for solving AP Mechanics problems?

The formula for solving AP Mechanics problems is ΔTy = ΔVy/Vy0, where ΔTy is the change in time, ΔVy is the change in velocity, and Vy0 is the initial velocity.

What information is needed to solve an AP Mechanics problem?

To solve an AP Mechanics problem, you will need the initial velocity (Vo), the change in velocity (ΔVy), and the change in time (ΔTy).

How do you find the minimum time interval for an AP Mechanics problem?

To find the minimum time interval, you will need to use the formula ΔTy = ΔVy/Vy0. Plug in the given values for Vo and ΔVy, and solve for ΔTy. This will give you the minimum time interval needed to solve the problem.

What are some common mistakes when solving AP Mechanics problems?

Some common mistakes when solving AP Mechanics problems include not using the correct formula, not properly converting units, and not considering the direction of the velocity change. It's important to carefully read the problem and double check your work to avoid these mistakes.

How can I improve my problem-solving skills for AP Mechanics?

To improve your problem-solving skills for AP Mechanics, it's important to practice regularly and familiarize yourself with different types of problems. You can also seek help from a teacher or tutor to better understand the concepts and techniques used in solving AP Mechanics problems.

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