Solving the Drag Race Problem: Car A's Top Speed vs. Car B

[Chunkysalsa]

Homework Statement

Its a project where I have to create a scenario in which a dragster (Car A) has the highest top speed but loses the race(to Car B)

That is all that is given to me, although some random things such as Apocalypses or random explosions are obviously not permitted.

Homework Equations

I'm pretty clueless here but I guess the equations for acceleration and distance would be useful.

V=D/T
A=V/T
Vf=Vi + AT
Df=Di + ViT + 1/2(at^2)
Vf^2=Vi^2 + 2AD

V=Velocity, D=Distance, T=Time, A=Acceleration

The Attempt at a Solution

I've been drawing graphs left and right here trying to figure out a solution, from what I'm getting it seems like that if the cars are accelerating constantly then the faster car has to win unless some thing effects it such as releasing the parachute early, etc.
One idea I have is that Car A starts off going faster and accelerating faster but releases the parachute early and Car B overtakes it while still going under Car A's fastest speed. All I really need is an idea on what could happen and help graphing it. Everything else I can take care of my self.




This is really killing me because I have to do this project for tomorrow and I have a million other things going on at once. So any help would be appreciated greatly. Sorry if it seems like I haven't tried hard enough by myself. Its just that I'm low on time and I've run out of ideas. I totally fail at Physics, don't know why since I'm pretty good at other sciences and maths. I also must compliment on the nice site, I'll be looking at it in the near future if I can get past this day ^_^

 

[Kurdt]

If it has a higher top speed what would cause the car to not beat car b? There could be several answers. For example car b could accelerate quicker. I'm not sure what this project consists of. Do you have to think of a reason why car A would not win and then explore the physics behind it? Or just think of as many reasons how car A would not win?

 

[Chunkysalsa]

Yes, I have to think of a way for Car B to finish in less time and reach a lower top speed then Car A. Then I have to write what happened like a sports commentator and like you said explore the physics behind why Car B won and had a lower speed and prove it with graphs and math

Its just that I don't know exactly how to graph something like that. I mean how can I draw a Position vs Time graph and still make sure that Car B doesn't exceed the highest velocity of Car A.

 

[Kurdt]

You're going to have to make a series of assumptions for this. I would suggest you assume that car A accelerates constantly and reaches its top speed just before the finish line. I would then suggest you break car B's motion into two parts. The first part is where car B accelerates to its top speed which is less than car A's, and the second part where it completes the rest of the course at a constant speed. Using the kinematic equations you should be able to work out how fast car A & B accelerate etc.

If you're using velocity time graphs, you know the distance covered is the area under the graph. Since the cars must cover the same distance you can investigate what graphs will give the same area with less velocity and less time. Then it should be fairly easy to make up some commentary using the graphs.

 

[Chunkysalsa]

Okay thanks, now I have a physics question that's relating to this but I ultimately need to know. Let's say that a Car has a constant acceleration of 20m/s^2 what would be its distance in 1 seconds? In 2?

Time-Distance-Velocity
1-?-20m/s
2-?-40m/s

Is the velocity right? I am totally confused here, would the distance be 10m or 20m in one second and for 2seconds would it be 80m or 40m?

Using the equations V=D/T and A=V/T, I get 20m for 1s and 80m for 2s, however if I use the equation D=1/2(at^2) and If I calculate the area under a Velocity v Time graph then I get 10m for 1s and 40m for 2s. What am I doing wrong in this case?

Thanks for all the help again, I actually had to skip school because I can figure this out. So I'll have to finish this today and email it or something.

 

[Kurdt]

To deal with the constant acceleration problem you will need the kinematic equations given in this post.

https://www.physicsforums.com/showpost.php?p=905663&postcount=2

Since they start from rest the distance will be given by the acceleration term.

$$x=\frac{1}{2}at^2$$

 

[Chunkysalsa]

So then at 1s the car is at 10m right? Somehow that doesn't make sense to me, since if he's going 20m/s at 1s shouldn't he have moved 20m?

But numbers don't lie

 

[Kurdt]

They would only have moved 20m if they had a constant velocity of 20m/s, but of course they started from rest, so most of the time they are traveling less than 20m/s.

 

[Chunkysalsa]

Hmm, that's makes sense. Thanks alot, I figure since I'm having trouble visualizing and graphing this, I should make a table with all the values I need so I can see what's happening at ever second. Then I can graph anything and everything from it.