#43 An object travels along a line so that its position s is s = t2+ 1 meters after t seconds.
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An object travels along a line so that its position s is s = t2+ 1 meters after t seconds.
(a) What is its average velocity on the interval 2 ⤠t ⤠3?
(b) What is its average velocity on the interval 2 ⤠t ⤠2.003?
(c) What is its average velocity on the interval 2 ⤠t ⤠2 + h?
(d) Find its instantaneous velocity at t = 2.
Step 1 - We are told that we have an object whose position is given by the equation:
, where is in seconds.
Step 2 - (a) We are first tasked with determining its average velocity for time between 2 and 3.
To find an average velocity, we need to know the time interval which has taken place and the distance traveled in that time interval.
In the present case, the time interval is 1 second.
So our task is to find the distance traveled.
Step 3 - We can plug each of our values for time into the equation to get the corresponding positions of the object:
And
Step 4 - So we can see that the total distance the object has traveled between times and is:
Step 5 - So our average velocity is the total distance traversed over the given time interval, or:
Step 6 - (b) Next, we are tasked with finding the average velocity between time and time.
Step 7 - Again, to find an average velocity, we need to know the time interval which has taken place and the distance traveled in that time interval.
In the present case, the time interval is 0.003 seconds.
So our task is to find the distance traveled.
Step 8 - We found previously that the objectâs position at time is .
To find the objectâs position at,
We use our provided equation:
Step 9 - So we can see that the total distance the object has traveled between time and is:
meters
Step 10 - So our average velocity is the total distance traversed over the given time interval, or:
Step 11 -(c)Next, we are tasked with finding the average velocity between time and time .
Step 12 - Again, to find an average velocity, we need to know the time interval which has taken place and the distance traveled in that time interval.
In the present case, the time interval is seconds.
So our task is to find the distance traveled.
Step 13 - We found previously that the objectâs position at time is 5 meters.
To find the objectâs position at, we use our provided equation:
Step 14 - So we can see that the total distance the object has traveled between time and is:
meters
Step 15 - So our average velocity is the total distance traversed over the given time interval, or:
Step 16 -(d) Finally, we are tasked with finding the objectâs instantaneous velocity when.
Step 17 - We recall the definition of instantaneous velocity as:
, where is the position function
Using this definition and our provided position function, we have:
Step 19 -
Get the Free Online Chemistry Q&A Questions And Answers with explain. To crack any examinations and Interview tests these Chemistry Questions And Answers are very useful. Here we have uploaded the Free Online Chemistry Questions. Here we are also given the all chemistry topic.
ChemistryExplain team has covered all Topics related to inorganic, organic, physical chemistry, and others So, Prepare these Chemistry Questions and Answers with Explanation Pdf.
Question
An object travels along a line so that its position s is s = t2+ 1 meters after t seconds.
(a) What is its average velocity on the interval 2 ⤠t ⤠3?
(b) What is its average velocity on the interval 2 ⤠t ⤠2.003?
(c) What is its average velocity on the interval 2 ⤠t ⤠2 + h?
(d) Find its instantaneous velocity at t = 2.
Answer
Step 1 - We are told that we have an object whose position is given by the equation:
, where is in seconds.
Step 2 - (a) We are first tasked with determining its average velocity for time between 2 and 3.
To find an average velocity, we need to know the time interval which has taken place and the distance traveled in that time interval.
In the present case, the time interval is 1 second.
So our task is to find the distance traveled.
Step 3 - We can plug each of our values for time into the equation to get the corresponding positions of the object:
And
Step 4 - So we can see that the total distance the object has traveled between times and is:
Step 5 - So our average velocity is the total distance traversed over the given time interval, or:
Step 6 - (b) Next, we are tasked with finding the average velocity between time and time.
Step 7 - Again, to find an average velocity, we need to know the time interval which has taken place and the distance traveled in that time interval.
In the present case, the time interval is 0.003 seconds.
So our task is to find the distance traveled.
Step 8 - We found previously that the objectâs position at time is .
To find the objectâs position at,
We use our provided equation:
Step 9 - So we can see that the total distance the object has traveled between time and is:
meters
Step 10 - So our average velocity is the total distance traversed over the given time interval, or:
Step 11 -(c)Next, we are tasked with finding the average velocity between time and time .
Step 12 - Again, to find an average velocity, we need to know the time interval which has taken place and the distance traveled in that time interval.
In the present case, the time interval is seconds.
So our task is to find the distance traveled.
Step 13 - We found previously that the objectâs position at time is 5 meters.
To find the objectâs position at, we use our provided equation:
Step 14 - So we can see that the total distance the object has traveled between time and is:
meters
Step 15 - So our average velocity is the total distance traversed over the given time interval, or:
Step 16 -(d) Finally, we are tasked with finding the objectâs instantaneous velocity when.
Step 17 - We recall the definition of instantaneous velocity as:
, where is the position function
Using this definition and our provided position function, we have:
Step 19 -
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