A car rolls along the x-axis, and its position is given by x =5 + 8t - 5 . What

Question

A car rolls along the x-axis, and its position is given by x =5 + 8t - 5 . What was its displacement during the time interval between t = 0 and 2 s? What was the total distance traveled during the same time interval? Hint: The car changed directions. What was the car's average velocity during this time interval? Docs the quantity equal the average velocity during this time interval? Is this car's acceleration constant? A car rolls along the x-axis, and its position is given by x =5 + 8t - 5 . What was its displacement during the time interval between t = 0 and 2 s? What was the total distance traveled during the same time interval? Hint: The car changed directions. What was the car's average velocity during this time interval? Docs the quantity equal the average velocity during this time interval? Is this car's acceleration constant?

Explanation / Answer

i ) x = 5 + 8t - 5t^2 A ) for displacement , simply substitute t=2 in the given equation the answer is 1 unit B ) for total distance , u will simply change the ( -5t^2 ) to a positive number , i . e. ; take the absolute value of the given equation. the answer is 41 unit C ) average velocity = total displacement / time taken total displacement from part A is 1 , time taken is 2 seconds , so the answer is 1/2 D ) NO e ) yes it is , taking the second order derivative of the given equation , it will give you another equation for the acceleration; a ( t ) = -10 . notice that it is independent of t , and hence constant ii ) for this parts i will just write the answers, because its the same procedure. a ) 2 b ) 1 c ) No d ) No , a ( t) = - 30 t , dependent on t , so acceleration is not constant i hope it helps :) if you need to know more about anything else related to this , let me know.

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