3. a 2kg wooden block whose initial speed is 3 m/s slides on a smooth floor for 2 meters before it comes to a
stop.
a. find the coefficient of friction?
b. how much force would be needed to keep the block moving at a constant speed across the floor?

Calculating Coefficient of friction is 0.229.

Force is 4.5 N that keep the block moving at a constant speed.

Explanation:

We know that speed expression is as .

Where, is initial speed, V is final speed, ∆s displacement and a acceleration.

Given that,

=3 m/s, V = 0 m/s, and  ∆s = 2 m

Substitute the values in the above formula,

0 = 9 - 4a

4a = 9

is the acceleration.

Calculating Coefficient of friction:

Compare the above equation

Cancel "m" common term in both L.H.S and R.H.S

Hence coefficient of friction is 0.229.

calculating force:

F = 4.5 N

Therefore, the force would be 4.5 N to keep the block moving at a constant speed across the floor.