Velocity of derivation, Mathematics

Velocity : Recall that it can be thought of as special case of the rate of change interpretation. If the situation of an object is specified by f(t ) after t units of time the velocity of the object at t = a is given by f ′ ( a ) .

Example   Assume that the position of an object after t hours is specified by,

                                          g (t ) =t/t+1

Answer following

(a) Is the object moving towards the right or the left at t = 10 hours? 

(b) Does the object ever stop moving? 

 Solution; The derivative is,               g ′ (t ) = 1 /(t + 1)2

 (a) Is the object moving towards the right or the left at t = 10 hours?

To find out if the object is moving to the right (velocity is positive) or left (velocity is negative) we require the derivative at t = 10 .

                                                             g′ (10) =1 /121

Thus the velocity at t = 10 is positive and hence the object is moving to the right at t = 10 .

(b) Does the object ever stop moving?

If the velocity is ever zero then the object will stop moving.  Though, note that the only way a rational expression will ever be zero is if the numerator is zero. As the numerator of the derivative (and therefore the speed) is constant it can't be zero.

Then, the object will not at all stop moving.

Actually, we can say little more here. The object will be moving always to the right as the velocity is always +ve.

Here we've seen three major interpretations of the derivative.  You must remember these, specially the rate of change, as they will continually show up throughout this course.

Posted Date: 4/12/2013 2:30:51 AM | Location : United States







Related Discussions:- Velocity of derivation, Assignment Help, Ask Question on Velocity of derivation, Get Answer, Expert's Help, Velocity of derivation Discussions

Write discussion on Velocity of derivation
Your posts are moderated
Related Questions
Proof of Sum/Difference of Two Functions : (f(x) + g(x))′  = f ′(x) +  g ′(x)  It is easy adequate to prove by using the definition of the derivative.  We will start wi

you are driving on a freeway to a tour that is 500 kilometers from your home. after 30 minutes , you pass a freeway exit that you know is 50 kilometer from your home. assuming that

In addition and subtraction we have discussed 1) Some ways of conveying the meaning of the operations of addition and subtraction to children. 2) The different models o


find the diameter of circle whose circumference is 26.51

A vessel in shape of a inverted cone is surmounted by a cylinder has a common radius of 7cm this was filled with liquid till it covered one third the height of the cylinder. If the

You plan to retire when you are 65th years old.  You are now 25 years old.  You plan to buy a pension annuity that will pay you $100,000 per year starting one year after you turn 6

The following graph shows the growth of the median home value in a particular region of the United States starting in 1996.  The graphs starts in 1996 and shows the trend through t


If sin? =  1/2 , show that 3cos?-4cos 3 ? = 0. Ans:    Sin ? = ½ ⇒ ? = 30 o Substituting in place of ? =30 o . We get 0.