Velocity/Acceleration word problem. I'm so confused

In summary, the problem presents a scenario where the individual is traveling at 20 m/s and approaches a yellow light at an intersection. They must decide whether to brake or speed up before reaching the intersection, which is photo-enforced and will result in an $85 traffic ticket if the light is run. The total time to make this decision cannot exceed 5 seconds, with a 1 second reaction time. The intersection is 15m wide and the acceleration rate is 2m/s^2. The individual must either travel less than 50m if they brake or more than 50m if they speed up in this time. If they choose to brake, their velocity will decrease by 5 m/s every second until reaching 0
  • #1
bammeh
3
0

Homework Statement


You are traveling at 20 m/s and the stop light turns yellow. You have to make an insantaneous decision: Do i brake before the intersection or do I hit the gas pedal and beat the light? Keep in mind that this particular intersection is photo-enforced, and an $85 traffic ticket will be issued if you run the stop light.

total time must not exceed 5 seconds
You have a 1 second reaction time.
The intersection is 15m wide.
When you first saw the light turn yellow, you were 50m in front of the intersection.
Acceleration rate is 2m/s^2
Deceleration rate is 5m/s^2



Homework Equations


a= vf-vi/t


The Attempt at a Solution



If you stop at the light:

Time Action Velocity
0 Saw Light Turn 20m/s
1 Reaction 15 m/s
2 10m/s
3 5 m/s
4 0 m/s
5 -5 m/s

If you try to beat the light:

Time Action Velocity
0 Saw Light Turn 20 m/s
1 Reaction 22m/s
2 Hit the Gas 26m/s
3 Speed Up 32 m/s
4 Speed Up 40 m/s
5 Speed Up 50 m/s

There are more questions but this is the main part i am unsure about. :/
 
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  • #2
[tex]x=v_ot+\frac{1}{2}at^2[/tex]
You can use that. If he decides to stop he needs to travel less than 50m in the time.
If he decides to speed up he needs to travel more than 50m during that time.

In the second part, your acceleration is constant at 2. You went all over the place with your acceleration.
 
  • #3
What is vo?

Sorry, she doesn't teach much. she just hands out the paper and tells us to complete it.

also, what are you finding? (what is x standing for? Velocity? Acceleration?)
 
  • #4
Vo is your initial velocity and x is the distance traveled.
 
  • #5
Alright, I'll work on this in a few minutes and let you know what I get.

I'm trying to find the velocity though.

With a beginning velocity of 20 m/s and in increase of 2m/s^2

I get the answers:

Time Velocity
0 20 m/s
1 22m/s
2 26m/s
3 32 m/s
4 40 m/s
5 50 m/s

But you said it was constant so it should be:

20
22
24
26
28
?
 

What is velocity and acceleration?

Velocity refers to the rate of change in an object's position over time. It is a vector quantity, meaning it has both magnitude (speed) and direction. Acceleration, on the other hand, refers to the rate of change in an object's velocity over time.

How do you solve velocity/acceleration word problems?

To solve these types of problems, you will need to identify what is known and what is unknown, and then use the appropriate kinematic equations to solve for the unknown variable. It is important to pay attention to units and use the correct formula for the given scenario.

What are some common units for velocity and acceleration?

Velocity is typically measured in meters per second (m/s) or kilometers per hour (km/h). Acceleration is typically measured in meters per second squared (m/s^2) or kilometers per hour squared (km/h^2).

How does velocity and acceleration relate to each other?

Velocity and acceleration are related through the equation a = dv/dt, where a is acceleration, v is velocity, and t is time. This means that acceleration is the derivative of velocity with respect to time. In other words, acceleration is the rate of change in velocity.

What are some real-life examples of velocity and acceleration?

Velocity can be seen in everyday activities such as driving a car, riding a bike, or running. Acceleration can be observed in situations like a car speeding up or slowing down, a rollercoaster going up or down a hill, or a ball being thrown into the air.

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