Skip to main content

When can the instantaneous velocity of an object equal the average velocity of an object? I understand that if acceleration is zero, motion is...

As pointed out in the question, with uniform motion (no acceleration) the instantaneous velocity and the average velocity are the same everywhere, as the object has a constant rate of change in regards to its distance traveled.


But there can be times when the instantaneous velocity and average velocity are the same even with varying accelerations. For example, imagine a 300 mile road trip which takes exactly 5 hours. The average speed (velocity if the...

As pointed out in the question, with uniform motion (no acceleration) the instantaneous velocity and the average velocity are the same everywhere, as the object has a constant rate of change in regards to its distance traveled.


But there can be times when the instantaneous velocity and average velocity are the same even with varying accelerations. For example, imagine a 300 mile road trip which takes exactly 5 hours. The average speed (velocity if the trip is all in one direction) is 60 miles per hour. Your speed at any time of the trip could be 60 miles per hour; it might always be 60 miles per hour, or you might speed up and slow down.


This is the premise behind giving speeding tickets to vehicles whose speed has been measured indirectly. Some police utilize markings on the pavement and a flying spotter while others might time a trip between toll stations, etc., but they never measure speed directly. They infer that a vehicle that covers a distance faster than they could have covered it obeying the speed limit must have exceeded the speed limit. Further they know that the vehicle must have reached the average velocity during the trip.


Using ideas from calculus we can show that if the distance function can be modeled by a continuous (no breaks or asymptotes) curve with no corners or cusps over an interval from a to b, then there is a point c in the interval where the velocity (the instantaneous rate of change of the distance at point c) will be equal to the average velocity (the average rate of change over the interval).


You can see this graphically; the curve represents the distance function as a function of time while the line shows the instantaneous velocity for some points:



Comments

Post a Comment

Popular posts from this blog

What is the meaning of "juggling fiends" in Macbeth?

Macbeth is beginning to realize that the three witches have been deceiving him since he first encountered them. Like jugglers, they have kept changing their forecasts in order create confusion. This is particularly apparent when the Second Apparition they raise in Act IV,   Scene 1 tells him that no man of woman born can overcome him in hand-to-hand battle--and then Macbeth finds himself confronted by the one man he has been avoiding out of a... Macbeth is beginning to realize that the three witches have been deceiving him since he first encountered them. Like jugglers, they have kept changing their forecasts in order create confusion. This is particularly apparent when the Second Apparition they raise in Act IV,   Scene 1 tells him that no man of woman born can overcome him in hand-to-hand battle--and then Macbeth finds himself confronted by the one man he has been avoiding out of a sense of guilt, and that man tells him: Despair thy charm. And let the angel whom thou still hast serve...
Post a Comment
Read more

In Martel's Life of Pi, how does writing a diary help Pi Patel build on his leadership skills?

At the end of chapter 73, Pi first divulges the fact that he had started a diary after about a week alone at sea. Pi claims that he wrote about "practical stuff" (208) such as what he caught for food, foreseeable problems and solutions, Richard Parker, and reflections about specific events that occurred. In a sense, Pi is the captain of his ship; therefore, he must take responsibility for himself and his crew. He can... At the end of chapter 73, Pi first divulges the fact that he had started a diary after about a week alone at sea. Pi claims that he wrote about "practical stuff" (208) such as what he caught for food, foreseeable problems and solutions, Richard Parker, and reflections about specific events that occurred. In a sense, Pi is the captain of his ship; therefore, he must take responsibility for himself and his crew. He can do this by writing down events, problems and solutions, and reflections to look back on when confronted with repeated problems. It can ...
Post a Comment
Read more

Why did Tybalt attack and kill Mercutio instead of Romeo, who he had originally been targeting?

Though Tybalt's quarrel is with Romeo, he begins the momentous duel in Act 3 by fighting with and killing Mercutio instead. Tybalt ultimately attacks Mercutio because the garrulous and hot-headed character insults Tybalt and goads him into a duel to protect Romeo's honor. From the beginning of the encounter in Act 3, Scene 1, it's clear that Mercutio is itching for a fight. For instance, when Tybalt signals that he wants to talk to Mercutio... Though Tybalt's quarrel is with Romeo, he begins the momentous duel in Act 3 by fighting with and killing Mercutio instead. Tybalt ultimately attacks Mercutio because the garrulous and hot-headed character insults Tybalt and goads him into a duel to protect Romeo's honor. From the beginning of the encounter in Act 3, Scene 1, it's clear that Mercutio is itching for a fight. For instance, when Tybalt signals that he wants to talk to Mercutio and Benvolio, Mercutio responds "And but one word with one of us?/ Couple it w...
Post a Comment
Read more