A hockey puck struck by a hockey stick is given an initial speed v_{0} in the positive x-direction. The coefficient of kinetic friction between the ice and the puck is μ_{k}.

(a) Obtain an expression for the acceleration of the puck. (Use the following as necessary: μ_{k} and g.)

a

=

(b) Use the result of part (a) to obtain an expression for the distance d the puck slides. The answer should be in terms of the variables v_{0}, μ_{k}, and g only.

(a) The
acceleration is not dependent on the initial velocity of the puck, so
you'll use Newton's 2nd law to find the magnitude of the acceleration.
Since the only force (ignoring resistance from the air) is the friction
between puck and ice. Also, the friction force is negative because it
acts against the direction of motion, the equation is:

∑F = ma = -μmg
a = -μmg / m
a = -μg

(b) Use the time-independent kinematics equation:

v² = v₀² + 2aΔx

Substituting -μg for a and solving for Δx (remember, v, final velocity, is zero because the puck comes to rest):