# Quadratic Equations and kinetics

1. May 2, 2010

### mode656

1. The problem statement, all variables and given/known data
Find the time required for a train to reach 100m if V0=20m/s and acceleration is
0.5m/s2

2. Relevant equations
s=v0t+(1/2)at2

3. 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:(

2. May 2, 2010

### rock.freak667

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

0.25t2+t-5 = 0

at2+bt+c=0

3. May 2, 2010

### 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

4. May 2, 2010

### Squeezebox

$$\Delta$$x=vit+$$\frac{1}{2}$$at2

There's your kinematic equation.

Edit: sorry didn't see your attempt.

$$\Delta$$x=vit+$$\frac{1}{2}$$at2

0=vit+$$\frac{1}{2}$$at2-$$\Delta$$x

$$\frac{1}{2}$$at2+vit-$$\Delta$$x=0

5. May 2, 2010

### mode656

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

6. May 2, 2010

### Squeezebox

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

7. May 2, 2010

### 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

8. May 2, 2010

### rock.freak667

Multiply your equation throughout by 4.

9. May 2, 2010

### mode656

any specific reason why? or is it just so?

10. May 2, 2010

### rock.freak667

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.