Solve Sliding Hockey Puck Problem: Coeff. of Kinetic Friction

[kchurchi]

Homework Statement

A hockey puck is sliding across a frozen pond with an initial speed of 7.5 m/s. It comes to rest after sliding a distance of 23.7 m. What is the coefficient of kinetic friction between the puck and the ice?

v_0x = initial speed = 7.5 m/s
v_fx = final speed = 0 m/s
Δx = x distance traveled = 23.7 m
f_k,IP = force of kinetic friction from ice on puck
N_IP = normal force from ice on puck
W_EP = weight force from Earth on puck
m_P = mass of puck
g = acceleration due to gravity

Homework Equations

ƩF_net = m*a
ƩF_x = -f_k,IP = m*a_x
ƩF_y = N_IP - W_EP = m*a_y → a_y = 0 m/s^2 → N_IP = m_P*g

The Attempt at a Solution

I attempted this logic...

f_k,IP = μ_k*N_IP → (-m*a_x)/(m_P*g) = μ_k

But then I hit a wall when trying to find the x-acceleration. Help?

 

[voko]

You need the equation of distance traveled under constant acceleration (deceleration in this case).

 

[kchurchi]

I am not allowed to have the equations of constant acceleration to solve problems. I must derive all equations myself using calculus. How do I even know that the acceleration is constant?

 

[SHISHKABOB]

there's only one force acting on the puck in the x-direction: the frictional force

and it depends on two constant values: the coefficient of friction and the normal force on the puck

therefore, the force is constant, therefore the acceleration is constant

set up the equation of motion

\Sigma F = m\ddot{x} = F_{friction}

and go from there

I'm assuming that since they want you to derive the equations yourself, that you know how to do a differential equation, right?