How to find the path and acceleration if the mass, time, force and coefficient of friction are known?

Given:

t is the time of body movement (seconds);

k is the coefficient of friction;

F is the force acting on the body (Newton);

g is the acceleration of gravity;

m – body weight (kilogram).

It is required to determine the body’s acceleration a (m / s2) and its traversed path S (meter).

Since it is not specified in the problem statement, we assume that the body begins to move without an initial velocity. Then, we define the acceleration of the body:

F – F friction = m * a;

F – k * m * g = m * a;

a = (F – k * m * g) / m.

Let’s find the path traversed by the body:

S = a * t ^ 2/2 = (F – k * m * g) * t ^ 2 / (2 * m).

Answer: the acceleration of the body will be equal to a = (F – k * m * g) / m, the path traversed by the body will be equal to S = (F – k * m * g) * t ^ 2 / (2 * m).