A body with a mass of 1 kg under the action of a constant force moves in a straight line, the dependence of the path

A body with a mass of 1 kg under the action of a constant force moves in a straight line, the dependence of the path traveled by the body on time has the form s = t ^ 2 + 2t + 2 determine the work 5 seconds after the start of its action.

Let us assume that in the conditions the path is expressed in meters, and the time is in seconds. Calculating the second derivative of the path, we find the acceleration with which the body moved:

a = (t ^ 2 + 2t + 2) ” = (2t + 2) ‘= 2 m / s2.

That is, the movement of a body of mass m occurred with a constant acceleration a under the action of a constant force F. According to Newton’s second law:

F = ma = 1 * 2 = 2 N.

Path s5 traversed in time t = 5 s:

S5 = 5 ^ 2 + 2 * 5 + 2 – 02 – 2 * 0 – 2 = 50 m.

The job you are looking for:

A = FS5 = 2 * 50 = 100 J.

Answer: 100 J.