Assume that the coefficient of static friction between the board and the box is not known at this point. What is the magnitude of the acceleration of the box in terms of the friction force f?

Explanation:

From Newton's second Law of Motion,

F = ma

Ff + F = ma

Where F is the applied force, Ff is the frictional force, a is the acceleration and m is the mass of the object or box.

Magnitude of the acceleration:

a = Ff+F/m

This must act in the direction of F or the box would slide or accelerate off the negative side of the board (taking the direction of F to be positive

think about the oscillation of the toy shown in the video. when the toy is at the highest point of its motion, its velocity is zero and its acceleration is negative.

the bal will not change its velocity.