8) A cart launched horizontally across a surface with an initial speed of 16.0 m/s, where the
surface has variable friction such that the kinetic coefficient is of the form μ = 0.15(1 + 0.4x)
where 0.4 has units of m. a) Derive an expression for the acceleration of the system. b) Derive
an expression for the velocity of the system. How far will the cart move before coming to rest?
Assume the initial position is the origin. Bonus: Find how long the cart will move before coming
to rest. NOTE: This is hard, hence why it is bonus. Note: Bowling alleys have variable friction,
so the ball is gripped differently at different points of the lane.