   Chapter 12.3, Problem 12E

Chapter
Section
Textbook Problem

# Finding Velocity and Acceleration Vectors in Space In Exercises 11-20, the position vector r describes the path or an object moving in space.(a) Kind the velocity vector, speed, and acceleration vector of the object.(b) Evaluate the velocity vector and acceleration vector of the object at the given value of t. Position Vector Time r ( t ) = 3 t i + t j + 1 4 t 2 k t = 2

(a)

To determine

To Calculate: The velocity vector, speed, and acceleration vector of the object.

Explanation

Given:

The given position vector and time is Position vector r(t)=3t.i^+t.j^+14t2.k^,   t=2

Calculation:

The derivative of the given position vector is:

r(t) is r'(t)=3.i^+j^+12t.k^

Now derivative of the velocity vector to get acceleration:

r'(t) isr''(t)=12

(b)

To determine
The velocity vector and acceleration vector of the object at the given value of t.

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