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## Homework Statement

"3. A car traveling 20 m/sec [fwd] is involved in a collision and stops over a distance of 1.8 meters. (This is a comparatively calm collision.)

a) What is the acceleration of the car during this collision?

b) What force is necessary to hold a 70 kg adult in her seat during the collision?

c) Assume an adult is wearing her seatbelt and holding a 15 kg child on her lap. What force must the adult exert to hold this child during the collision? Could you exert this large of a force?"

So I see I've been given

v[itex]_{1}[/itex] = 20 m/s

v[itex]_{2}[/itex] = 0 m/s

d = 1.8m

## Homework Equations

I have a few equations I could use here, or that I think I could use.

First off I was thinking

d = [(v

_{1}+v

_{2})/2] · t

to find t and then using

a = v

_{2}- v

_{1}/ t

in order to find a

And then I thought about the

v

_{2}= v

_{1}+ 2ad

which I could rearrange into

a = (v

_{2}-v

_{1}) / 2d

## The Attempt at a Solution

I decided to try both.

-----------------------------------------------------------------------------------------------

1.8 = [(20)/2] · t

t = 0.18s

so with an average speed of 10m/s it takes 0.18s to go 1.8m

a = (0-20)/0.18

a = -111.11 m/s

^{2}

so if it takes 0.18s go to from 20 to 0 m/s the accel it would seem is -111.11m/s

^{2}

-----------------------------------------------------------------------------------------------

and then I tried the other equation

a = (0-20) / 2(1.8)

a = - 5.56 m/s

^{2}

I should mention that although I have seen people justify the second equation, I'm still quite iffy about it because it just doesn't make sense to me on its own, whereas the other equations do.

The two answers are pretty different. I ignored sigfigs throughout this because I didn't think it was entirely relevant to my problem. So whats going on here? I'm sure I screwed up somewhere, somehow.