Question

Due to a force field, a particle of 10kg moves along a space curve where position vector is given in a function of time by (4t^3)i ̂+(5t^2)j ̂+(t^2)k ̂

a. ) What is the velocity vector?

i ̂ j k ̂

b. ) Calculate for the momentum.

i ̂ j k ̂

Answer 1

a. ) The velocity vector is the first derivative of the position vector:

$$\vec v(t)=12t^2\hat i+10t\hat j+2t\hat k.$$

b. ) The momentum is velocity times mass:

$$\vec p(t)=m\vec v(t)=120t^2\hat i+100t\hat j+20t\hat k.$$