A crate of mass m is gently placed with zero initial velocity on an inextensible conveyor...

Apply the equilibrium equation in the direction.

Here, is the mass of the crate, and is the normal force.

Apply the Newton’s second law equation in the direction.

Here, is the acceleration, and is the frictional force.

Apply the friction law for slip, assuming that.

Substitute for.

Here, is the coefficient of kinetic friction between the crate and conveyor.

Substitute for.

(a)

Calculate the distance the crate slides before it stops by assuming constant acceleration.

Here, is the initial velocity, is the final velocity.

Substitute for, for and 0 for.

Therefore, the distance the crate slides before it stops slipping is.

(b)

Calculate the stopping time.

Substitute for, for and 0 for.

Therefore, the time it takes for the crate to stop is.