A container of mass 0.3 kg slides along the ice with a speed of 4 m/s when it reaches a rough section where the coefficient of kinetic friction is 0.8. How long will it take the puck to stop sliding?

a = -.8 g

v = 4 - .8(9.81) t
at v = 0
t = 4/[.8*9.81)

To find out how long it will take for the container to stop sliding, we need to determine the deceleration of the container due to friction.

We can calculate the deceleration using the formula:

acceleration = coefficient of friction * acceleration due to gravity

The acceleration due to gravity is approximately 9.8 m/s^2.

Since the container is moving in the opposite direction of its initial velocity, the net acceleration will be negative.

acceleration = -0.8 * 9.8 m/s^2 = -7.84 m/s^2

Next, we can use the formula of motion:

final velocity = initial velocity + (acceleration * time)

We know that the final velocity is 0 m/s (since the container stops sliding), the initial velocity is 4 m/s, and the acceleration is -7.84 m/s^2.

0 = 4 + (-7.84 * time)

Simplifying the equation, we have:

-7.84 * time = -4

Dividing both sides of the equation by -7.84, we get:

time = -4 / -7.84

Calculating the result, we find:

time ≈ 0.51 seconds

Therefore, it will take approximately 0.51 seconds for the container to stop sliding.