Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I'm reading Stewart's Essential Calculus:

EXAMPLE 1 Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of the ball after 5 seconds.

SOLUTION Through experiments carried out four centuries ago, Galileo discovered that the distance fallen by any freely falling body is proportional to the square of the time it has been falling. (This model for free fall neglects air resistance.) If the distance fallen after seconds is denoted by and measured in meters, then Galileo’s law is expressed by the equation

$$s(t)= 4.9t^2$$

The difficulty in finding the velocity after 5 s is that we are dealing with a single instant of time $(t=5)$ , so no time interval is involved. However, we can approximate the desired quantity by computing the average velocity over the brief time interval of a tenth of a second from $t=5$ to $t=5.1$:

What he meant with difficulty here?

share|improve this question

2 Answers 2

up vote 5 down vote accepted

He means that whereas it's easy to define the average velocity over a period (as displacement divided by time), it's much harder to define instantaneous velocity. So instead of thinking initially about an instantaneous velocity, he considers the average velocity over a very short period of time.

share|improve this answer

Average velocity has clear physical content: it is change in displacement divided by elapsed time. Instantaneous velocity is more of a theoretical construct: there is no clear way that such a thing could be measured.

share|improve this answer
    
Isn't instantaneous velocity just $v_{avg}=\frac{\Delta d}{\Delta t}=\frac{d_f-d_i}{t_f-t_i}$? –  Vÿska Sep 30 '12 at 2:51
4  
That fraction only makes sense if $t_f\neq t_i$, but that means that you're not looking at an instant. –  user22805 Sep 30 '12 at 2:56
    
It may be a very dumb question, but why can't we just $t$ for $5$ in $s(t)= 4.9t^2$? –  Vÿska Sep 30 '12 at 23:28
1  
Here, $s(t)$ stands for displacement (that is, the distance fallen), not velocity or speed. –  user22805 Sep 30 '12 at 23:48

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.