Velocity and acceleration - three dimensional space, Mathematics

Assignment Help:

Velocity and Acceleration - Three Dimensional Space

In this part we need to take a look at the velocity and acceleration of a moving object.   

From Calculus I we are familiar with that given the position function of an object that the velocity of the object is the 1st derivative of the position function and the acceleration of the object is the 2nd derivative of the position function. 

Thus, given this it shouldn't be too surprising that whether the position function of an object is specified by the vector function  r→(t) then the velocity and acceleration of the object is illustrated by,

v (t) = r'(t)

a (t) = r'' (t)

Note: The velocity and acceleration are as well going to be vectors also.

In the study of the motion of objects the acceleration is frequently broken up into a tangential component, aT, and the normal component denoted as aN.  The tangential component is the part or element of the acceleration which is tangential to the curve and the normal component is the part of the acceleration which is normal or orthogonal to the curve.  If we do this we can write down the acceleration as,

a = aT T+ aNN

where T and N stands for the unit tangent and unit normal for the position function.

If we illustrate v = ||v (t)|| then the tangential and normal components of the acceleration are specified by,  

aT = v' =r' (t).r''(t) /(||r' (t)||)

aN = kv2 = ||?r' (t) *r" (t)|| / ||r' (t)||

in which k is the curvature for the position function.

There are two (2) formulas to employ here for each component of the acceleration and when the second formula may seem excessively complicated it is frequently the easier of the two.  In the tangential component, v, might be messy and calculating the derivative may be unpleasant.  In the normal component we will previously be computing both of these quantities in order to get the curvature and thus the second formula in this case is certainly the easier of the two.


Related Discussions:- Velocity and acceleration - three dimensional space

Method of cylinders or method of shells, Method of cylinders or method of s...

Method of cylinders or method of shells The formula for the area in all of the cases will be,                                                        A = 2 ∏ ( radius ) (heig

Alegrabra, how do you do algebra with division

how do you do algebra with division

RECTILINEAR FIGURES, AB,BC,CD ARE THREE CONSECUTIE SIDES OF REGULAR POLYGON...

AB,BC,CD ARE THREE CONSECUTIE SIDES OF REGULAR POLYGON.IF ANGLE BAC IS 18 DEGREE, FIND EXTERIOR ANGLES AND NUMBER OF SIDES ?

Multiplication of binomials, To understand the multiplication of binomials,...

To understand the multiplication of binomials, we should know what is meant by Distributive Law of Multiplication. Suppose that we are to multiply (a + b) and m. We

Define symmetric, Define symmetric, asymmetric and antisymmetric relations....

Define symmetric, asymmetric and antisymmetric relations.    Ans: Symmetric Relation A relation R illustrated on a set A is said to be a symmetric relation if for any x,

Determine the widest piece of mail, A mailbox opening is 4.5 inches high an...

A mailbox opening is 4.5 inches high and 5 inches wide. Determine the widest piece of mail able to ?t in the mailbox without bending? a. 9.5 inches b. 2.2 inches c. 6.7 in

Fermat''s little theorem, 1. How many closed necklaces of length 7 can be m...

1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent

Randi takes the stairs at work whenever possible instead, Randi takes the s...

Randi takes the stairs at work whenever possible instead of the elevator. She must climb up 51 steps from her office to get to the accounting department. The human resources depa

Find the initial number of balls, Balls are arranged in rows to form an equ...

Balls are arranged in rows to form an equilateral triangle .The first row consists of one ball, the second two balls and so on.   If 669 more balls are added, then all the balls ca

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd