Help with time/acceleration problem

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Homework Help Overview

The problem involves an object starting from rest and accelerating with constant acceleration. The object accelerates for a time \( t \) and then continues to accelerate for an additional second. The distance traveled during the time \( t \) is stated to be half of the distance traveled during the one-second interval. Participants are tasked with finding the time \( t \).

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss relationships between distance and time under constant acceleration, exploring various equations related to the problem. Some question their understanding of the relationships and attempt to manipulate equations to find \( t \). Others express confusion about their calculations and the assumptions made regarding distances.

Discussion Status

The discussion is ongoing, with participants sharing their attempts and questioning their reasoning. Some have provided guidance on using specific equations, while others are exploring different setups and interpretations of the problem. There is no explicit consensus on the correct approach yet.

Contextual Notes

Participants note potential misunderstandings regarding the relationships between the distances and the time intervals involved. There is also mention of a specific answer that one participant believes is correct, but they are unsure how to arrive at it based on the information given.

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Homework Statement


An object starts from rest at the origin and accelerates for a time t (x axis). Acceleration is constant. Object continues with same acceleration for an additional one second. The distance traveled during time t is one half the distance traveled during the one second interal' Find the time t.


Homework Equations


These are guesses. Total time = t+1.0s.
Total distance = x + 1/2x = 1.5x



The Attempt at a Solution


I haven't been able to figure this out. I keep going in circles.
 
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Welcome to PF.

What is the relationship between distance and time for an object under constant acceleration?
 
LowlyPion said:
Welcome to PF.

What is the relationship between distance and time for an object under constant acceleration?

I've been playing with these equations: v = 1.5x/(t+1.0s)
a = (1.5x)/(t+1.os)2

Am I on the right path?
 
nathan scott said:
I've been playing with these equations: v = 1.5x/(t+1.0s)
a = (1.5x)/(t+1.os)2

Am I on the right path?

I would prefer to see you rely on the relationship that x = 1/2*a*t2
 
LowlyPion said:
I would prefer to see you rely on the relationship that x = 1/2*a*t2

I think I'm doing something fundamentally wrong because I try:

1.5x = 1/2* 1.5x/(t+1.0s)2*(t+1)2
But then I end up with 1.5x = 0.75x, which is obviously incorrect.
Something isn't clicking with me and this problem.
 
Not quite.

You have 3/2*(1/2*a*t2) = 1/2*a*(t + 1)2

Just solve for t. Eliminating 1/2*a directly :

3/2 t2 = (t + 1 )2

Take the square root of both sides ...
 
LowlyPion said:
Not quite.

You have 3/2*(1/2*a*t2) = 1/2*a*(t + 1)2

Just solve for t. Eliminating 1/2*a directly :

3/2 t2 = (t + 1 )2

Take the square root of both sides ...

I don't think it works. This ends up being : (the squared root of 6)/2*t = t + 1.
The x variable I was using in 1.5x was under the assumption that distance x + 1/2x = Total X. So I don't think I can plug 1/2*a*t2 into the 1.5x, or 3/2x side of the equation. What do you think?
 
The 1/2 a*t2 is already the distance you call x.

The 3/2*x then is 3/2*(1/2*a*t2) and from the statement of the problem that's the same as !/2*a*(t + 1)2

As to the answer you got, I'd recheck your math.
 
I appreciate your help but I'm still confused. I'll keep pluggin away at it. I tried a different setup for time. I tried Total time = t, one portion of t (for distance x) would be 1.0s and the other distance (1/2*x)would be t-1.0s. I'm just not sure how to solve for t with the information supplied in the problem. I know the answer is 1.37s but I can't figure out how to arrive at that.
 
Last edited:
  • #10
I think I see the problem. I made the same mistake.

The statement of the problem says that

xt = 1/2*(xt+1 - xt)

This means that

3xt = xt+1

not 3/2.
 

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