Question

The positions of particle moving along a straight path is s(t)=5+62 +7eset+secht (where s is in feet and 120 is in seconds). A) Find the average velocity of the particle from 1 to 6 seconds. Include the correct units. B) Find the instantaneous velocity of the particle after 6 seconds. Include the correct units. C) Find the average rate of change of the velocity of the particle from 1 to 6 seconds. Include the correct units. D) Find the instantaneous acceleration of the particle after 6 seconds. Include the correct units. E) When t=6 seconds, is the particle speeding up or slowing down? Explain. Without the correct explanation, your score in question 3) may be zero.

Answer 1

Due to typos or errors in the provided function, it's not clear how to calculate the requested quantities. However, conceptually these quantities could be found using calculus-based techniques for a properly defined function.

Step-by-step explanation:

Unfortunately, the stated function s(t)=5+62 +7eset+secht is not clearly defined, and appears to contain typos or errors. Therefore, it's not possible to calculate the average velocity, instantaneous velocity, average rate of change of the velocity, or instantaneous acceleration of the particle. Conceptually, these quantities could be found using calculus-based techniques if we had a properly defined function. For instance, the average velocity over a time interval [a,b] could be found by determining the net displacement (final position minus initial position) divided by the total time elapsed.

Instantaneous velocity at a certain time could be found by taking the derivative of the position function at a given time. The average rate of change of velocity or mean acceleration over a time interval [a,b] could be calculated as the change in velocity divided by the time elapsed. The instantaneous acceleration at a certain time could be found by taking the derivative of the velocity function at a given point in time.

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