1. Understand the Forces

* Friction: The only horizontal force acting on the object is kinetic friction, which opposes its motion.

* Newton's Second Law: The object's acceleration is caused by the net force acting on it.

2. Set up the Equations

* Friction Force: F_friction = μ * N (where μ is the coefficient of kinetic friction and N is the normal force)

* Normal Force: Since the table is horizontal, the normal force is equal to the object's weight: N = mg (where m is mass and g is acceleration due to gravity, approximately 9.8 m/s²)

* Newton's Second Law: F_net = ma (where a is the acceleration)

3. Solve for Acceleration

* Since the only force acting horizontally is friction, F_net = F_friction.

* Combining the equations: μ * mg = ma

* Canceling mass (m) on both sides: μ * g = a

* Calculate the acceleration: a = 0.3 * 9.8 m/s² = 2.94 m/s²

4. Use Kinematics to Find Initial Velocity

* We know:

* final velocity (v_f) = 0 m/s (comes to rest)

* time (t) = 1.3 s

* acceleration (a) = -2.94 m/s² (negative since it's slowing down)

* Use the kinematic equation: v_f = v_i + at

* Solve for initial velocity (v_i): v_i = v_f - at

* Plug in the values: v_i = 0 - (-2.94 m/s²)(1.3 s) = 3.82 m/s

Therefore, the initial velocity of the object was 3.82 m/s.