Understanding t_max in the Drag Racer Problem

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Homework Help Overview

The discussion revolves around a physics problem involving a drag racer accelerating from rest while another car approaches at a constant speed. The primary focus is on understanding the concept of t_max, which is the maximum time after the dragster begins to accelerate that the approaching car can collide with it.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the meaning of t_max, questioning whether it refers to the moment of collision or another point in time. There is discussion about the implications of the dragster starting to accelerate at the last possible moment and how that affects the timing of the collision.

Discussion Status

Some participants have proposed interpretations of t_max, suggesting it relates to the distance traveled by both vehicles at the moment of potential collision. Others express confusion regarding the problem's wording and the assumptions that can be made, indicating a lack of consensus on how to approach the problem.

Contextual Notes

Participants note the ambiguity in the problem regarding the initial distance between the two vehicles and the timing of the dragster's acceleration. There is also mention of the need to clarify the conditions under which the collision occurs, as well as the implications of the dragster's acceleration on the outcome.

jcsp101
Problem:
To demonstrate the tremendous acceleration of a top fuel drag racer, you attempt to run your car into the back of a dragster that is "burning out" at the red light before the start of a race. (Burning out means spinning the tires at high speed to heat the tread and make the rubber sticky.)

You drive at a constant speed of v_0 toward the stopped dragster, not slowing down in the face of the imminent collision. The dragster driver sees you coming but waits until the last instant to put down the hammer, accelerating from the starting line at constant acceleration, a. Let the time at which the dragster starts to accelerate be t=0.

Question 1:
What is t_max, the longest time after the dragster begins to accelerate that you can possibly run into the back of the dragster if you continue at your initial velocity?

My Question:
What does the problem mean by t_max?
is it like the time when the drag racer and car touch, or when they both reach their max velocity, or what?
 

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The drag racer is accelerating away from the car while the car ismoving towards it at a constant velocity, so the question asks, as I interpret it, what is the maximum time interval between that the drag racer initiating acceleration and its being hit by your car.
 
What confuses me about this problem, is we don't know when "the last instant" is. It could be 1 metre before the car hits the dragster, could be when the d between the front of the car, and the tail of the dragster is 0 (at which point they'd ht, but I'd still call this the last instant).

I can't see any assumptions to be made. If we don't know when the dragster starts to accelerate, or the distance from the car to the dragster, I can't see how this can be done.

I could make an elaborate formula with a few constants chucked in, but I don't know if that's correct.
 
wow nvm, i sort of somehow figured out that first one is = to v_0 over a, altho I am stull not sure what tmax is...

this is the next one tho:
Assuming that the dragster has started at the last instant possible (so your front bumper almost hits the rear of the dragster at t= t_max), find your distance from the dragster when he started. If you calculate positions on the way to this solution, choose coordinates so that the position of the drag car is 0 at t = 0. Remember that you are solving for a distance (which is a magnitude, and can never be negative), not a position (which can be negative).

but i still don't quite get tmax, cause i thought that WHEN they touched, the drag racer accelerated or something, so how does this make sense?
 
Last edited by a moderator:
The problem asks for the 'maximum' time. That implies that the dragster guns it at the very instant the car is just about to hit it. You must calculate the time it takes for each to be touching each other, one accelerating, the other moving at constant speed. HINT: what can you say about the distance traveled by each when they touch?
 
when they touch, the car has already traveled (i assume) v_o*tmax ?
but the dragster hasnt technically moved at all right?
 
jcsp101 said:
when they touch, the car has already traveled (i assume) v_o*tmax ?
but the dragster hasnt technically moved at all right?
Oh, wait, sorry, i messed that up, forget my previous post. I agree with all that something is missing in this problem, and am also confused.
 
yea eh, so now its this second problem whcih makes no sense since idk what Tmax is yet...
woo, got an hour an a half to try to figure it out.

gg, thanks anyway lol...
 
jcsp101 said:
when they touch, the car has already traveled (i assume) v_o*tmax ?
but the dragster hasnt technically moved at all right?
Yes and no. I believe the problem is saying that after a certain amount of seconds have passed (t_max), the car can never hit the dragster, because it's speed will have equaled the speed of the car at that time, and will exceed it in the next instant, so the car can never catch it. So yourr answer for t_max = v_o/a appears correct, and the car will have traveled v_o*t_max. However, the dragster must already have moved a distance from his start equal to 1/2(a)t_max^2 during that period. A confusingly worded problem, if you ask me.
 
  • #10
Hey there! I have the same problem and was able to get the first part of t_max=v_0/a, however I am really confused on how to even approach the second question:Assuming that the dragster has started at the last instant possible (so your front bumper almost hits the rear of the dragster at ), find your distance from the dragster when he started. If you calculate positions on the way to this solution, choose coordinates so that the position of the drag car is 0 at . Remember that you are solving for a distance (which is a magnitude, and can never be negative), not a position (which can be negative). I'm not sure how to calculate the distance if it seems as if they will never touch because the dragster's speed will have to have equaled the car's speed at that instant of time. How am I supposed to solve for the distance D_start?
 

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