Posted by **Hannah** on Saturday, September 12, 2009 at 1:31pm.

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.

- Physics-calc -
**MathMate**, Saturday, September 12, 2009 at 5:33pm
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^2**i** - 6.0t^3**j**) 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.

- Physics-calc -
**Hannah**, Saturday, September 12, 2009 at 6:56pm
What it P representing? Position?

- Physics-calc -
**Kim**, Thursday, February 18, 2016 at 6:13pm
6t-18t

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