# Find Acceleration with only Initial Velocity and Final position?

## Homework Statement

A hockey puck sliding on a frozen lake comes to rest after 238 m. If its initial velocity is 3.8 m/s what is its acceleration if it is assumed constant? Answer in units of m/s^2

How long is it in motion? What is its speed after traveling 180 m?

## Homework Equations

x=xo + vot +1/2at^2

## The Attempt at a Solution

v^2=(vo)^2+2a(x-xo)
...v^2=(3.8)^2 + 2a (-238)

but i don't know the velocity, cause i don't have the time!

3.8 m/s * 1/238 m = time?

I find that I can't do anything without the time! I'm so lost and confused. PLEASE HELP.

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diazona
Homework Helper
Here's a hint: what does "comes to rest" mean? ;-)

LowlyPion
Homework Helper

## The Attempt at a Solution

v^2=(vo)^2+2a(x-xo)
...v^2=(3.8)^2 + 2a (-238)

but i don't know the velocity, ...
Welcome to PF.

That equation works. Your final velocity is 0 so ...

v2 = 3.82 = 2*a*238

Then you have your acceleration a.

With that v = a*t so t becomes easy to find.

To find the speed at 180 m just use the equation you gave above to determine the speed at that distance.

Welcome to PF.

That equation works. Your final velocity is 0 so ...

v2 = 3.82 = 2*a*238

Then you have your acceleration a.

With that v = a*t so t becomes easy to find.

To find the speed at 180 m just use the equation you gave above to determine the speed at that distance.
But then we have two variables, a, and v, how do I solve then? it doesn't work if you manipulate and substitute v =at because then the other variable, t, comes in.

diazona
Homework Helper
But then we have two variables, a, and v,
No you don't, you only have one, a. Look carefully at the equation LowlyPion wrote for you.

No you don't, you only have one, a. Look carefully at the equation LowlyPion wrote for you.
ok, i tried it, solved for a and I got .030 m/s^2 = a.

i typed that into my homework answers, and it said it was incorrect (we have multiple times to try it)

and when I do v=at,

3.8=(.030)t,

I get 125.3 seconds....seems a bit too much time. am i doing something wrong?

LowlyPion
Homework Helper
ok, i tried it, solved for a and I got .030 m/s^2 = a.

i typed that into my homework answers, and it said it was incorrect (we have multiple times to try it)

and when I do v=at,

3.8=(.030)t,

I get 125.3 seconds....seems a bit too much time. am i doing something wrong?
I trust you entered it as a = -.03 m/s2

It is decelerating after all.