**Acceleration of Block against Friction**

Newton’s second law says that the acceleration (a) of an object is proportional to the force (F) applied on it, and the proportionality factor is the object’s mass (m). Force is a vector quantity, which means we must consider the direction in which it acts. Two main types of frictional forces exist: The static force and the sliding force.

**a) Acceleration of a block on Horizontal Surface: **When body is moving under application of force P, then kinetic friction opposes its motion.

Let,
a is the net acceleration of the body, from the figure ma = P – F_{k} ⇒ \(a\,=\frac{P-{{F}_{k}}}{m}\).

**b) Acceleration of a block sliding down over a rough Inclined Plane: **When angle of inclined plane is more than angle of repose, the body placed on the inclined plane slides down with acceleration (a).

From the figure: ma = mg sin θ – F ⇒ ma = mg sin θ – μR

⇒ ma = mg sin θ – μmg sin θ

Therefore, Acceleration (a) = g (sin θ – μ cos θ)

**c) Retardation of a block sliding up over a rough Inclined Plane: **When angle of inclined plane is less than angle of repose, then for the upward motion,

⇒ ma = mg sin θ + F ⇒ ma = mg sin θ + μ mg cos θ

Retardation, (a) = g (sin θ + μ cos θ)