# please teach the concept of speed and velocity

### Asked by Akkala Padmavathi | 7th Apr, 2012, 07:00: PM

What's the difference between two identical objects traveling at different speeds? Nearly everyone knows that the one moving faster (the one with the greater speed) will go farther than the one moving slower in the same amount of time. Either that or they'll tell you that the one moving faster will get where it's going before the slower one. Whatever speed is, it involves both distance and time. "Faster" means either "farther" (greater distance) or "sooner" (less time). Doubling one's speed would mean doubling one's distance traveled in a given amount of time. Doubling one's speed would also mean halving the time required to travel a given distance. If you know a little about mathematics, these statements are meaningful and useful. (The symbol *v* is used for speed because of the association between speed and velocity, which will be discussed shortly.)

- Speed is directly proportional to distance when time is constant:
*v*?*s*(*t*constant) - Speed is inversely proportional to time when distance is constant:
*v*? ?*t*(*s*constant)

Combining these two rules together gives the definition of speed in symbolic form.

v = |
s |
(Note: this is not the final definition.) | |

t |

### velocity

But Wait, there's more! In order for you or me to calculate the speed of an object we must know how far it's gone and how long it took to get there. Astute observers should then ask a following question

What do you mean by "how far"? Didn't we learn in the previous section that there are two quantities that can be used to answer the question "how far"?

My but you are wise. Yes indeed, there are two ways to answer that question. When you ask "how far" are you asking for the *distance* or the *displacement*? There's a difference between the two quantities and thus a difference between the two answers. To further ruin your life, we're even going to use two different words.

- Speed is the rate of change of
*distance*with time. - Velocity is the rate of change of
*displacement*with time.

Which means that for the calculus people

- Speed is the first derivative of
*distance*with respect to time. - Velocity is the first derivative of
*displacement*with respect to time.

### Answered by | 9th Apr, 2012, 10:17: AM

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