- #1

AnnaRiddle

## Homework Statement

A car is moving with a constant velocity of 18 m/s for 5 seconds, if in the next 5 seconds it travels a distance of 40 m, what is its final velocity?

## Homework Equations

Δx= vit+ 1/2 at^2

vf= vi+at

**vf^2 = vi^2 + 2a (Δx)**## The Attempt at a Solution

So I tried doing it different ways and I got -2 m/s in all of them, but by doing a velocity vs time graph it seems that +2 m/s is the right answer. Here's how I did it:

I first solved for acceleration from this formula:

Δx= vit+ 1/2 at^2, using 40 m as my Δx, 18 m/s as my starting velocity and 5 seconds for time, which gave me an acceleration of -4 m/s^2.

With that, I then plugged in vf= vi+at and got -2 m/s. But when I do it using this formula vf^2 = vi^2 + 2a (Δx) I get + 2 m/s.

My question is, is there a way to know exactly which direction it will go by only doing it algebraically? (I mean without doing the graph) also, why am I getting different signs? I can't seem to find the gap in my two processes.