# Finding velocity as a function of position, constant acceleration

**1. The problem statement, all variables and given/known data**

A truck is traveling down the road at 60 mph, and begins to decelerate at a rate of 0.8 g.

I’d like to find the total distance it takes the truck to stop, and come up with a formula for the velocity as a function of displacement from the original braking point.

**2. Relevant equations**

I think that the relevant equation is v^{2} = 2a(s_{2}-s_{1})+v_{1}^{2}

**3. The attempt at a solution**

Well, I know the truck is traveling at 88 fps, and slowing at a rate of 0.8 * 32fps^{2}, so it will take

88 fps / (32.2 fps^{2} * 0.8 g) * 44 fps = 150 feet to stop

But when I plug those numbers into the above equation, I get

v_{2} = (2 * (0.8 * 32.2 * 60 / 88) * (-x) + (60)^{2})^{0.5}

That has the right y-intercept (65 mph), but the wrong x-intercept, around 104′

If I change the "2" on the right side of the equation to 1.38, it looks right, but I can’t work out why it would be 1.38 instead of two.

Argh! Any help much appreciated!

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