Physicscalc
posted by Hannah on .
Suppose the position of an object is given by >r(vector) = (3.0t^2*ihat  6.0t^3*jhat)m. Where t in seconds.
Determine its velocity >v as a function of time t.
Determine its acceleration >a as a function of time t.
Determine >r at time t = 2.5 s.
Determine >v at time t = 2.5s.
Express your answer using two significant figures. Express your answer in terms of the unit vectors ihat and jhat.

This is a problem of differentiation where the independent variable is t, and
r is the position vector.
v is the velocity vector.
a is the acceleration vector.
The motion is described in two orthogonal directions i and j, which means that you can do the calculations in each of the directions independently of each other.
Given
r = (3.0t^2i  6.0t^3j) m
The i and j components of the position vector are
Pi(t)=3.0t^2
Pj(t)=6.0t^3
So d(Pi(t))/dt = d(3t²)/dt = 6t
...
can you complete the rest?
Post your answers for a check if you wish to. 
What it P representing? Position?

6t18t