What is the Time Equation for Constant Acceleration?

[kriegera]

Hi All - I am trying to find an equation that gives the time as a function of initial velocity, distance traveled, and specified acceleration. That is, t = some function of v(0), d, and a.

We ran a simulation problem for distances 25 and 50 meters and my times were - 4.099 and 6.141 respectively for initial velocity of 2.00 and inital acceleration of 2.00. i can't come up with any equations that fit my data. any input please?

Thank you!
Ashley

 

[Doc Al]

Review the basic kinematic equations, which relate those variables: https://www.physicsforums.com/showpost.php?p=905663&postcount=2"

 

[kriegera]

So would it be:
t=SQRT(2s-v(o)/a

s=distance
v(o)=inital velocity

I've tried this but it doesn't give me the exact anser - is it ok to round up or down? Initally I found final velocity and then plugged it in but the challenge is to use one equation. Input?

Thank you!

 

[Doc Al]

So would it be:
t=SQRT(2s-v(o)/a

The starting equation would be:
s = v₀t + 1/2at²

To find t you'll need to solve the quadratic.

 

[kriegera]

The starting equation would be:
s = v₀t + 1/2at²

To find t you'll need to solve the quadratic.

Thank you for this tip. I am not very "up" on my physics - this is my first introduction to it on a college level. What are the rules for solving for the quadratic? Does that involve derivitives? Thank you!

 

[Doc Al]

What are the rules for solving for the quadratic? Does that involve derivitives?

No need for calculus, just the 'quadratic formula'. (Google it!)

Note that I am assuming that your setup is one where the acceleration is constant. (You didn't actually state that.)

 

[kriegera]

Yes - acceleration is constant. I'll let you know what I find out. Thanks.