# Finding time given constant acceleration, initial velocity, & distance

## Homework Statement

I want to cover a distance of 8,ooo,ooo,ooo,ooo m and I want to know the time it will take if I have an initial velocity of 176400 m/ sec with an acceleration of 19.6 m/sec2. I think I have the right equation here I'm just not sure how to solve for t. Could someone walk me through the steps? Cheers.

## Homework Equations

D = 0.5* a * t2 + V0 * t

## The Attempt at a Solution

8000000000000 m = 0.5* 19.6 m/sec2 * t2 + V0 * t

8000000000000 m = 9.8 m/sec2 * t2 + 176400 m/ sec * t

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Simon Bridge
Homework Helper
That is correct - the equation is quadratic in t ... so, put it in standard form and use the quadratic equation:
$$ax^2+bx+c=0 \implies x\in \frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Would the standard form be: 9.8t2 + 176400t + 8000000000000

Last edited:
haruspex
Homework Helper
Gold Member
Would the standard form be: 9.8t2 + 176400t + 8000000000000
Not quite. Watch the signs.
Also, sounds like this could get relativistic. Are you supposed to consider that?

9.8t2 + 176400t - 8000000000000 (?)

If it gets relativistic then I guess I have to consider it. This isn't for homework or anything like that. This is just for something I'm writing. I just wanted a quick solution to what I thought was a simple problem but I can see that it's escalating into a big problem. Even this quadratic stuff is over my head to be honest.

Simon Bridge
Homework Helper
##(9.8)t^2 + (176400)t - (8000000000000)=0## .. these numbers look familiar.
Anyway: You posted this in the homework section - which produces a particular kind of response.

What education level are you at?

Sorry. The general section said that any homework/ course type questions should be posted here. Mine seemed to fit into that category.

I finished highschool a few years ago now but since I've never had reason to use anything above basic math I've forgotten most of what I learned regarding algebra.

I was really just looking for a way to calculate velocities. I did find a website to help me solve quadratic equations which, after putting in the variables from the standard form equation, has given me 894552.7270791921 and -912552.7270791921. I'm supposed to use the positive answer aren't I? So t = 894552 seconds. That sounds about right to me.

haruspex
Homework Helper
Gold Member
So t = 894552 seconds.
At which point the velocity will be about 6% the speed of light, right? So maybe no need to bother Herr Prof Einstein.

Thanks for your help guys. Now that I know what to do with those velocity equations I think I should be set.

Cheers.

Simon Bridge