General physics problem involving velocity, acceleration, braking of a car

[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.

 

[PhaseShifter]

This is similar to another question I saw here yesterday.
It's a two-part problem since the car doesn't begin to decelerate until the driver reacts. That's where the 0.75s comes in.

total distance traveled = distance covered before reaction + distance covered during deceleration

 

[tomcue]

I would first like to commend you on attempting to solve this physics problem on your own. It shows your determination and critical thinking skills. Let me provide some guidance to help you solve this problem.

Firstly, let's start by understanding the given information. You are driving a car at a velocity of 55 km/h, and you have a reaction time of 0.75 seconds to begin braking. The best deceleration rate you can achieve is 5.18 m/s^2. The problem also gives you the distance to the intersection and the duration of the yellow light for two scenarios.

To solve this problem, we will use the formula x = x0 + v0t + 0.5at^2, which you have mentioned in your third question. This is the formula for displacement, and it involves initial position (x0), initial velocity (v0), acceleration (a), and time (t).

Now, let's apply this formula to the given scenarios. In scenario a), the distance to the intersection is 40 m, and the duration of the yellow light is 2.8 seconds. We can plug in these values in the formula and solve for x, which represents the displacement of the car.

x = x0 + v0t + 0.5at^2
x = 0 + 15.277778 m/s * 2.8 s + 0.5 * 5.18 m/s^2 * (2.8 s)^2
x = 0 + 42.777778 m + 20.384 m
x = 63.161778 m

This means that the car will travel a distance of 63.161778 m before coming to a stop if you brake to a stop. However, if you choose to continue moving at 55 km/h, the car will travel a distance of 15.277778 m/s * 2.8 s = 42.777778 m before entering the intersection. Since this is less than the given distance of 40 m, you should continue moving at 55 km/h in this scenario.

Similarly, in scenario b), the distance to the intersection is 32 m and the duration of the yellow light is 1.8 seconds. Using the same formula, we can calculate the displacement for this scenario.

x = x0 + v0t + 0.5at^2