Time Taken for Moving 200m with Constant Speed of 10m/s

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Discussion Overview

The discussion centers on the problem of determining the time taken for a person moving a distance of 200 meters at a constant speed of 10 m/s, with a focus on the equations of motion. Participants explore the implications of constant acceleration and the conditions under which time can be solved from the equations.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses difficulty in rearranging the equation S = ut + 1/2at² to isolate t using only letters, suggesting a need for a general method.
  • Another participant notes that if acceleration (a) is zero, the equation simplifies to S = ut, allowing for t to be expressed as t = S/u.
  • Some participants propose that if acceleration is not zero, the equation becomes quadratic, and t can be solved using the quadratic formula.
  • Concerns are raised about the validity of the equation S = ut + 1/2at² when a = 0, questioning whether it can be used to derive t in such cases.
  • There is a discussion about the limitations of the quadratic formula when a = 0, with some participants arguing that a piecewise function may be necessary to accurately describe the relationship between variables.
  • One participant highlights that if the discriminant of the quadratic equation is less than zero, it indicates that a real value for t cannot be obtained, suggesting physical implications for the scenario described.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method for solving for t when acceleration is zero versus when it is not. Multiple competing views remain regarding the applicability of the equations and the conditions under which they can be used.

Contextual Notes

Participants express uncertainty about the assumptions underlying the equations and the conditions necessary for their application, particularly regarding the treatment of acceleration in the context of solving for time.

adjacent
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NOT a home work
A person moves with constant speed of 10m/s(Initially as well as finally). His acceleration is therefore zero.Distance moved is 200meter.Find time taken.I tried to use the equation below but had difficulty making t the subject
S=ut+1/2at2
a=Acceleration
t=time
u=speed
S=Distance moved
If I use the values given I could easily make t the subject
That is 200=10t+1/2*0*t2
Giving 200=10t (t=200/10) that is t=s/u in this case

I can't make t the subject using letters ONLY.There should be a way
 
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If a man travels for 2 hours at 60 mph, how far does he go? What equation do you need to solve that question?
 
hi adjacent! :smile:
adjacent said:
S=ut+1/2at2

I can't make t the subject using letters ONLY.There should be a way


if a ≠ 0, this is a quadratic equation, which you can solve with t = -b ± √(b2 - ) etc

if a = 0, it's simply s = ut, so t = s/u :wink:
 
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tiny-tim said:
if a ≠ 0, this is a quadratic equation, which you can solve with t = -b ± √(b2 - ) etc
if a = 0, it's simply s = ut, so t = s/u :wink:

S=ut+1/2at2
That means t cannot be made the subject of the formula by methods I use with (S=1/2(u+v)t)Etc?
What if S=ut+1/2at2 is given and asked to solve for t?
 
Last edited:
yes, solve it as a quadratic equation!
 
adjacent said:
S=ut+1/2at2

What if S=ut+1/2at2 is given and asked to solve for t?

For example no values for a,u,tetc were given.I solve it as a quadratic,If a turn out to be 0 then It would be wrong.Right?Meaning the equation is wrong for non accelerating objects(when for t)but when solved for S it is right even for non accelerating objects.How is it?I need proof
 
Last edited:
i don't understand :confused:

show us your solution for the quadratic​
 
tiny-tim said:
i don't understand :confused:

show us your solution for the quadratic​
For example,
a=0
s=200m
u=10m/s
t=20s
I can solve the equation even when a=0,(for s)
S=ut+1/2at2
=10*20+1/2*0*202 =200m:smile:
But for t,
0.5at2+ut-s=0
t=(-b+√(b2-4ac)/2a
t=(-10+√(102-4(0)(-200))/(2*0) = MATH ERROR:confused:
In general If acceleration=0 - cannot solve for t
If acceleration≠0 - can solve for t
If acceleration is either ≠or= -can solve for S
Why?
 
adjacent said:
In general If acceleration=0 - cannot solve for t
If acceleration≠0 - can solve for t
If acceleration is either ≠or= -can solve for S
Why?

because the quadratic formula (-b ± √etc) does not work for a = 0
 
  • #10
tiny-tim said:
because the quadratic formula (-b ± √etc) does not work for a = 0
But if it can be solved for S,There should be some method to solve for t too.(Except t=s/u which is obtained once you know the value of a)
Just Algebra(Only letters)?
 
  • #11
adjacent said:
But if it can be solved for S,There should be some method to solve for t too.(Except t=s/u which is obtained once you know the value of a)
Just Algebra(Only letters)?

tiny-tim answered your question in post #3. There are two cases: a = 0 and a ≠ 0.

If a = 0, then t = s/v.
If a ≠ 0, then you can solve for t by using the quadratic formula.
 
  • #12
adjacent said:
But if it can be solved for S,There should be some method to solve for t too.(Except t=s/u which is obtained once you know the value of a)
Just Algebra(Only letters)?

A quadratic equation means that a≠0.
##0x^2 + 2x + 4## is not a quadratic.
 
  • #13
adjacent said:
But if it can be solved for S,There should be some method to solve for t too.(Except t=s/u which is obtained once you know the value of a)
Just Algebra(Only letters)?

I see what you're saying, and the answer to it is that the quadratic expression given by t = ... isn't quite complete because it assumes [itex]a\neq 0[/itex]. What we need is a piecewise function to describe it

If [itex]s = ut + 1/2at^2[/itex]

Then

[tex]t = <br /> \begin{cases}<br /> \frac{-u\pm \sqrt{u^2+2as}}{a}, & a\neq 0 \\<br /> \frac{s}{u}, & a=0<br /> \end{cases}[/tex]

You need to also keep in mind that if the discriminant is less than zero, which is [itex]a\neq 0[/itex] but [itex]u^2+2as<0[/itex] then you won't have a real value for t. Physically, this means that the object won't ever cross the line at displacement s because it would be accelerating away from that direction.
 

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