1. The problem statement, all variables and given/known data A particle of mass 2.0 kg has position given by the vector r = (t^4 -3t^3) i + (t^3 - 9t) j + (2t -6) k (where i, j, and k are the unit direction vectors and r is given in meters and t in seconds. At what time in seconds is the particle located at the origin? For this I get t = 3(seconds). It's the second part I want you to check. 1. what is the magnitude of the particle's velocity (in m/s) when the particle is at the origin? 2. For the particle in question 1, what is the x/y/z-component of the net force (in Newtons) acting on it when it is at the origin? Do not write Newtons as part of your answer. 2. Relevant equations V = Dr / Dt F= Ma 3. The attempt at a solution 1. Derive each component individually. Got: (4t^3-9t^2)i, (3t^2 - 9)j, (2)k Plug in 3 to get. 27 + 18 + 2 = Sqrt 47 = 6.86 m/s while at origin. 2. Derived each component again to get the acceleration eq. I got (12t^2 - 18t)i, (6t)j, and (0)k Then did F = MA for each component. 2.0(12(3)^2 - 18(3)) = 108 for x component. 2.0(6(3)) = 36 for the y component. 2.0(0) = 0 for the z component. Did I do this correctly? Thanks for helping :D.