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- Find the average speed over the time interval [1, 5] (time in seconds) of a particle whose position at time t is s(t) = t3 − 6t2 m.Given the function s(t)= -16t2 + 128t, what is the average velocity at time interval [1,2]? Then make a conjecture about the value of the instantaneous velocity at t=1.The average velocity between t=30 and t=30+h. f(t) =127850 -16t^2 for 0
- Q2. A particle moves along a straight line so that aftert (seconds), its distance from Oa fixed point on the line is S (meters), where S=t^3-9i) When is the particle at o?ii) What is the particle velocity and acceleration at these times?ii) What is its average velocity during the first second?iv) Whatis its average acceleration between t-0 and t= 3?The accompanying graph plots the best quadratic fit, a(t) = − 0.70t^2 + 1.44t + 10.44, to the data from the preceding table. Compute the average value of a(t) to estimate the average acceleration between t=0 and t=5.A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times doesthe particle pass through the origin? At which times is the particle instantaneously motionless (i.e., it has zerovelocity)?
- Consider the position function s(t)=−4.9t2+35t+16. Complete the following table with the appropriate average velocities and then make a conjecture about the value of the instantaneous velocity at Time Interval Average Velocity (2,3) (2,2.1) (2,2.01) (2,2.001) (2,2.0001) t=2.A particle moves along a straight line so that after t (seconds), its distance from Oa fixed point on the line is s (meters), where S-t^3-9ti) When is the particle at o?ii) Whatis the particle velocity and acceleration at these times?ii) What is its average velocity during the first second?iv) What is its average acceleration between t=0 and t=3?according to the Florida agency for workplace the monthly average number of uneploment claims in a certain country is given by N (t)= 22.16t^2 - 238.5t + 2005 where t is the number of years after 1990. A) During what year did the number of claims decrease? b)Find the relative extrema and interpret it.
- The 2011 Tōhoku, Japan earthquake is the newest deadliest earthquake. The power was equal as about 600.000.000 Hiroshima bomb. After the 9.0 magnitude earthquake, 900 aftershocks emerged and around 13,705 casualties had to lose their lives during the course. Because the earthquake so powerful, it has shifted our earth axis by 25 cm. 5. Based on this information, arrive to the conclusion on how much stronger was this earthquake in comparison with 2017 Mexico earthquake. Show work.Make a table of average velocity and the make a conjecture about instantaneous velocity at the indicated point s(t)=40sin2t at t=0For the position function, s(t)=-16t2+103t, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 1. time interval [1,2] [1,1.5] [1,1.1] [1,1.01] [1,1.001] average velocity