Type a short answer to each question In this section we lear

Type a short answer to each question. In this section, we learned that the speed of an object is a rate of change; specifically, the rate at which distance traveled changes as time changes. Think of at least three other rates of change, and describe specifically what they measure. Extra points if you come up with one that doesn\'t have a unit of time in it. Why does dimensional analysis work for calculations invoking rates\'? (Recall the we developed it as a method for converting units.) Take another look at your answer to Question 0 at the beginning, of this lesson. Would you change your answer now that you\'ve completed the lesson? How you summarize the topic of this lesson now? What questions do you have about this lesson?

Solution

Answer of question (1) :

Here first example of rate of change from our real life can be the relation between the age and height of a person.

So example if at 13 year age, height of a person was 140 cm and at age 28 , it is 170 cm, that means its rate of change of heiight is =(170-140 )/(28-13) = 30/15= 2 cm per year that is its rate of change of height.

SEcond example is the rate of change of size of a ballon with respect to its radius.

So initially if area of a ballon is 50 cm^2 and its radius is 3 cm and later if its area is 75 cm and radius is 8 cm, then its area is increasing at the rate of (75-50)/(8-3) = 25/5 = 5 cm^2 per cm that is its rate of change of its area with respect to its radius.

Another example is rate of change of volume of cyliner with respect to change in its height when its radius remains constant. So initially when the height was 5 cm, its volume was 212 cm^3 and when its height is increased to 10 cm then its volume becomes 232 cm^3, so its rate of change of volume with respect to height will be given as :

(232-212)/(10-5) = 20/5= 4 cm^3 per cm.