A 38 kg penguin is sliding across a patch of ice, starting at 13 m/s. If the coefficient of friction is .12, how far will the penguin slide before incomes to a halt.

To find out how far the penguin will slide before coming to a halt, we need to calculate the deceleration due to friction.

The formula to calculate the deceleration due to friction is:

acceleration_friction = coefficient_of_friction * acceleration_due_to_gravity

Given:
mass of the penguin (m) = 38 kg
initial velocity (u) = 13 m/s
coefficient of friction (μ) = 0.12

To calculate the acceleration due to gravity (g), we need to use the formula:

acceleration_due_to_gravity = 9.8 m/s^2

Now we can calculate the deceleration:

acceleration_friction = 0.12 * 9.8 m/s^2

Next, we need to calculate the time taken (t) for the penguin to come to a halt. We use the formula:

final velocity (v) = 0 m/s (since the penguin comes to a halt)
t = (v - u) / acceleration_friction

Plugging in the values, we have:

0 = (0 - 13) / (0.12 * 9.8)

Simplifying the equation gives us:

0 = -13 / (0.12 * 9.8)

To solve for t, we can multiply both sides by (0.12 * 9.8) to isolate t:

t = -13 * (0.12 * 9.8)

Finally, to find the distance (s) the penguin slides, we can use the equation:

s = u * t + (1/2) * acceleration_friction * t^2

Plugging in the values:

s = 13 * t + (1/2) * 0.12 * 9.8 * (t^2)

Substituting the value of t:

s = 13 * (-13 * (0.12 * 9.8)) + (1/2) * 0.12 * 9.8 * ((-13 * (0.12 * 9.8))^2)

Calculating further will give us the distance (s) that the penguin slides.

To find out how far the penguin will slide before coming to a halt, you can use the concept of work and energy. The work done against friction will equal the change in kinetic energy, causing the penguin to come to a halt.

The work done against friction can be calculated using the formula:

work = force x distance

The force of friction can be calculated using the coefficient of friction and the normal force. The normal force is equal to the weight of the penguin, which can be calculated by multiplying its mass (38 kg) by the acceleration due to gravity (9.8 m/s^2).

normal force = mass x gravitational acceleration

Substituting the given values:

normal force = 38 kg x 9.8 m/s^2

Next, we can calculate the force of friction using the equation:

force of friction = coefficient of friction x normal force

Substituting the given values:

force of friction = 0.12 x (38 kg x 9.8 m/s^2)

Finally, we can calculate the work done against friction using the formula above. Since the work done is equal to the change in kinetic energy (from initial kinetic energy to zero), we can equate the work done to 0.5 * mass * velocity^2 (initial kinetic energy).

work = 0.5 x mass x velocity^2

From this equation, we get:

force of friction x distance = 0.5 x mass x velocity^2

distance = (0.5 x mass x velocity^2) / force of friction

Substituting the given values and calculating:

distance = (0.5 x 38 kg x (13 m/s)^2) / (0.12 x (38 kg x 9.8 m/s^2))

After solving the equation, you will find that the penguin will slide for approximately 159.17 meters before coming to a halt.