Answer to Question #83932 in Mechanics | Relativity for Geldi

Question

A particle of Mass m moving in the x direction the particle is subjected to the force F= a-k where k is a positive constant write equation of motion

Answer 1

The equation of motion is:

$$x=s+vt+at^2/2,$$

where

$$s$$

- starting position (x-coordinate before motion, in our case is 0),

$$v$$

- initial velocity (in our case is 0),

$$a$$

- acceleration,

$$t$$

- time - the variable.

For particle with mass m the acceleration according to Newton's second law is

$$a=F/m=(a-k)/m,$$

which actually does not make any sense if 'a' that comes from the force (F= a-k) is acceleration. According to this expression the unit of measurement for 'F' is the same as for the 'a' and 'k'. In real world forces and accelerations are measured in different units.

The equation of motion is

$$x=F/m*t^2/2=(a-k)/m*t^2/2$$

If you can clarify the expression for the force F, simply substitute it for F in the first part of the answer.