# How to find acceleration from only initial and final velocity

tooperoo

## Homework Statement

A novice snowboarder who weighs 60kg is sliding down a 10 degree slope at a constant velocity of 8 m.s^-1.
When they reach the bottom of the slope, they slow down due to the kinetic friction between the snowboard and the snow.

Find the rate at which the skier is de accelerating once they are on the flat snow.

## The Attempt at a Solution

I found the coefficient of kinetic friction (0.176), but how can you calculate the rate of de acceleration?

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voko
How did you find the coefficient of friction?

tooperoo
Coefficient = force of friction / normal force?
Is that not right?

tooperoo
Crap just realized I left out the snowboarders weight (60kg)

voko
So what is the force of friction at the bottom then?

tooperoo
im sorry but i don't know how I would

voko
You did that for the slope. Why can't you do it for the bottom?

tooperoo
Isnt there no net force acting at the bottom?

I found it on the slope because there was a force pulling it down the slope, but there isn't anything at the flat

voko
The net force is zero on the slope, because the acceleration is zero. At the bottom, the snowboarder decelerates, which means the net force is not zero.

tooperoo
My free body diagram shows the normal force and the weight arrows, and a force acting backwards, a force I am assuming is the kinetic friction acting on the snowboarder, slowing him down.

is that correct? where do i go from there?

voko
Indeed, these are the forces acting on the snowboarder. You need to determine the acceleration.

tooperoo
I agree. I am just very unsure as to how i would go about that.
Thank you so much for your help so far!

voko
As always, ma = net force. Decompose that into X and Y directions, and see where that gets you. This is actually simpler than what you did on the slope, there is no trigonometry involved.

tooperoo
The net force would be coefficient of friction derived above, multiplied by the Normal force, yes? (but the answer would be negative as it is pointing in the negative x direction?)

And then just solve for a?

voko
Correct.

tooperoo
Thank you so much for your help! You're a life saver