A force of friction of 3.2N acts on a 1.1kg puck while it is sliding along a horizontal surface. If the initial velocity of the puck was 7.5 m/s , how far will the puck travel before coming to rest?

To find the distance the puck will travel before coming to rest, we need to use the equations of motion.

First, let's determine the acceleration (a) experienced by the puck due to the force of friction. We can use Newton's second law of motion:

F = m * a

Where:
F = Force of friction = 3.2N
m = Mass of the puck = 1.1kg

Solving for acceleration (a):

a = F / m

a = 3.2N / 1.1kg

a ≈ 2.909 m/s²

Next, we can use the equation of motion:

v² = u² + 2 * a * s

Where:
v = Final velocity (0 m/s as the puck comes to rest)
u = Initial velocity = 7.5 m/s
a = Acceleration = 2.909 m/s²
s = Distance traveled (what we want to find)

We can rearrange the equation to solve for s:

s = (v² - u²) / (2 * a)

Substituting the values:

s = (0² - 7.5²) / (2 * 2.909)

s = (-56.25) / 5.818

s ≈ -9.67 m

The negative sign indicates that the puck is moving in the opposite direction. Since distance cannot be negative, we can take the absolute value:

s ≈ 9.67 m

So, the puck will travel approximately 9.67 meters before coming to rest.