Question

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.

Answer 1

This is a problem of differentiation where the independent variable is t, and
<b>r</b> is the position vector.
<b>v</b> is the velocity vector.
<b>a</b> is the acceleration vector.

The motion is described in two orthogonal directions <b>i</b> and <b>j</b>, which means that you can do the calculations in each of the directions independently of each other.

Given
<b>r</b> = (3.0t^2<b>i</b> - 6.0t^3<b>j</b>) m
The <b>i</b> and <b>j</b> 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.

Answer 2

What it P representing? Position?

Answer 3

6t-18t