If the equation of trajectory of a body is r=t2i-5 t j - 2t2 · k m, What is the force that makes it move if its mass is 4kg?




According to the Newton´s second law:

F = m·a

We know the mass and know that the instantaneous acceleration is the derivative  of the instantaneous velocity, regarding instantaneous time and velocity, is the derivative of the vector of position regarding time.

a=dvdt   v=drdt

Deriving the first vector of position and then the velocity vector:

v=dt2·i-5t·j+2t2·kdt=2·t ·i - 5 · j - 4·t · ka=d2t ·i-5j-4t · kdt = 2·i - 4· k 

Replacing the expression of the second law:

F=4 kg·2·i - 4· k  m/sF=8·i - 16· k N

Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Related sections
F = m · a
v=limt0vavg=limt0r t=drdt
a=limt0aa=limt0v t=dvdt