Finding Time and Vf: Car chase problem

In summary, Kyle passed Cameron at time 0, but Cameron catches up to Kyle by 4 seconds later. Cameron's top speed is 2.0m/s/s.
  • #1
Benny98
2
0
Here's the problem I was given:
Kyle is driving at a constant 45.0 m/s when he passes his street racer friend, Cameron. After a 4.00 second delay to get the car started and into gear, Cameron starts chasing Kyle with a constant acceleration of 2.00 m/s/s. How far will Cameron have to drive to catch Kyle, what will be Cameron's top
velocity, and how long will Cameron drive?

Somehow we are supposed to use the quadratic formula.
We haven't done that in class with this type of problem, only parabolic problems, and I don't know how to correlate the two. (ax^2+bx+c) I don't have enough information to use an equation like Vf=Vi+at or Xf=1/2at^2+Vi+Xi either.

What I've tried so far:

With the three graphs given, I could find the small bit of rectangular area in the first 4 seconds, but that doesn't really help me find anything. I tried different ways of attempting to find the area of the triangle that's formed, but I'm getting answers that don't make sense.

Can someone please explain what I need to do in a step-by-step format? I'm not sure how to start this.
Thank you!
 
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  • #2
Benny98 said:
I don't have enough information to use an equation like Vf=Vi+at or Xf=1/2at^2+Vi+Xi
You do.
If Kyle passes Cameron at time 0, what is Kyle's position at time t? What is Cameron's position at time t (for t > 4s)?
 
  • #3
haruspex said:
You do.
If Kyle passes Cameron at time 0, what is Kyle's position at time t? What is Cameron's position at time t (for t > 4s)?

Kyle would be 45m further than Cameron for each 1 of the 4 seconds (or a total of 180m further) Cameron at t>4s would increase by 2.0m/s/s...
 
  • #4
Benny98 said:
Kyle would be 45m further than Cameron for each 1 of the 4 seconds (or a total of 180m further) Cameron at t>4s would increase by 2.0m/s/s...
No, I mean using the equations you quoted and said you had not enough information to use.

(This is weird. I replied on this thread 12 hours ago but my reply disappeared so I had to type it in again.)
 

1. What is the significance of finding time and Vf in a car chase problem?

Finding the time and final velocity (Vf) in a car chase problem is important because it helps determine how long it will take for the car to catch up to another car or object. It also gives insight into the speed and acceleration of the car during the chase.

2. How do you calculate time and Vf in a car chase problem?

To calculate time and Vf, you will need to know the initial velocity (Vi) of the car being chased, the distance between the two cars, and the acceleration of the car being chased. You can use the equation Vf = Vi + at to find the final velocity, and then use the equation d = Vit + 1/2at^2 to find the time it takes for the car to catch up.

3. What are the units for time and Vf in a car chase problem?

Time is typically measured in seconds (s) and final velocity is measured in meters per second (m/s) in a car chase problem.

4. How does the angle of pursuit affect the calculations for time and Vf?

The angle of pursuit does not directly affect the calculations for time and Vf, but it can impact the distance between the two cars and the acceleration of the car being chased. This, in turn, can affect the final results for time and Vf.

5. What other factors can affect the accuracy of the calculations for time and Vf in a car chase problem?

Other factors that can affect the accuracy of the calculations include the presence of obstacles or traffic, changes in the acceleration of the car being chased, and errors in measurement or calculation. It is important to consider these factors and make adjustments accordingly for more accurate results.

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