Quadratic Equations and kinetics

[mode656]

Homework Statement

Find the time required for a train to reach 100m if V₀=20m/s and acceleration is
0.5m/s²

Homework Equations

s=v₀t+(1/2)at²

The Attempt at a Solution

i am not sure of how to go about getting s=(20)t+(1/2)0.5t² into quadratic form for use in the quadratic formula
this is my solution without the quad formula
s=v₀t+(1/2)at²
100=(20)t+(1/2)0.5t²
5=t+(1/2)0.5t²
5=t+.25t²
5=t³
cube root of 5 is 1.71 which is def wrong:(

 

[rock.freak667]

5=t+.25t²
5=t³
cube root of 5 is 1.71 which is def wrong:(

Just bring the '5' on the other side to get

0.25t²+t-5 = 0

at²+bt+c=0

 

[mode656]

in my book its sets up the quadratic form as t²+80t-400=0
the answer is still wrong i get 10??

it is supposed to be 4.5

 

[Squeezebox]

\Deltax=v_it+\frac{1}{2}at²

There's your kinematic equation.

Edit: sorry didn't see your attempt.

\Deltax=v_it+\frac{1}{2}at²

0=v_it+\frac{1}{2}at²-\Deltax

\frac{1}{2}at²+v_it-\Deltax=0

Quadratic form

 

[mode656]

i know that's the equation but i need the quadratic formula to solve for time when only acceleration, distance and initial velocity is known

 

[Squeezebox]

i know that's the equation but i need the quadratic formula to solve for time when only acceleration, distance and initial velocity is known

Those are the only variables you need to know. I edited my above post, sorry for reposting what you knew.

 

[mode656]

don't worry about it. My problem does not lie within my use of the quadratic formula. My question is just pretty much how the book got t^2+80t-400=0
from 100=(20)t+(1/2)0.5t2

 

[rock.freak667]

don't worry about it. My problem does not lie within my use of the quadratic formula. My question is just pretty much how the book got t^2+80t-400=0
from 100=(20)t+(1/2)0.5t2

Multiply your equation throughout by 4.

 

[mode656]

any specific reason why? or is it just so?

 

[rock.freak667]

any specific reason why? or is it just so?

If you plan to manually factorize it, it is easier to find the factors.

So instead of factorizing (1/4)t²+20t-100=0, it is easier to factorize out t²+80t-400.

If you plan to use the quadratic equation formula, then it really does not matter what form you put it in.