(Section 4.3) Your task is to estimate how far an object traveled during the time interval 0 ≤t≤ 8, but you only have the following data about the velocity of the object. 0 1 2 3 4 5 6 7 8 time (sec) velocity (feet/sec) 2 6 10 11 14 17 18 21 23 (A) Using the left endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct help (units). Total distance traveled = (B) Using the right endpoint Riemann sum, find approximately how far the object traveled. Your answers must include the correct help (units). Total distance traveled =

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Speedometer readings for a vehicle (in motion) at 9-second intervals are given in the table. t (sec) v (ft/s) 0 26 9 23 18 16 27 18 36 19 45 23 Estimate the distance traveled by the vehicle during this 45-second period using the velocities at the beginning of the time intervals.distance traveled feet Give another estimate using the velocities at the end of the time periods.

Q) Two tanks are connected as shown in figure below. Starting from time t=0 the pumping process shown in figure was applied. Find the amount of salt in each tank as a function of time. 4 L/min 8 L/min 2N/L salt 50N Salt 20N Salt 4 L/mln 4 L/min 100 L 100 L T1 T2

The velocity v (in m/s) of a rocket measured at half second intervals is shown in the image below. Use central differences to approximate the acceleration (in m/s2 ) of the rocket at times t = 1.0 s and t = 1.75 s.

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Only part c

Suppose an automobile is moving with increasing velocity and that we measure the car's velocity every two seconds. Time (sec) 0 Velocity (ft/sec) 20 2 30 4 38 6 44 8 48 10 50 1. Use L5 to estimate the total distance the car has traveled during the ten seconds. 2. Is L5 an under- or over-estimate of the total distance the car has traveled during the ten seconds? How can you tell? 3. Use R5 to estimate the total distance the car has traveled during the ten seconds. 4. Is R5 an under- or over-estimate of the total distance the car has traveled during the ten seconds? How can you tell? 5. Find a better estimate for the total distance the car has traveled during the ten seconds.

Number 6

What's the difference between average velocity and instantaneous velocity? O Instantaneous velocity is greater than average velocity Average velocity is greater than instantaneous velocity O Average velocity is velocity over an interval of time while instantaneous velocity is velocity at one moment in time. O They're pretty much the same.

The table shows the position of a motorcyclist after accelerating from rest. t (seconds) (1) [2, 4] () [3, 4] (i) [4, 5] 0 (iv) [4, 6] ft/s s (feet) 0 (a) Find the average velocity (in ft/s) for each time period. ft/s ft/s 1 ft/s 2 3 4.9 10.7 23.2 4 50.3 5 109.4 6 237.6. (b) Plot the points in the table to create a graph of s as a function of t to estimate the instantaneous velocity (in ft/s) when t = 3. (Round your answer to one decimal place.) ft/s

4. DETAILS period ZILLDIFFEQMODAP11 5.1.008. ft cycles A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s. amplitude How many complete cycles will the mass have completed at the end of 57 seconds? MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

1. The barnacle falls off the wheel after 22.5 minutes. Use your regression equation to predict the height of the barnacle when it falls of the wheel,to the nearest tenth of a meter. 2. Determine the total time within the first rotation that the barnacle is at least 2 meters above the surface of the water, rounded to the nearest tenth of a minute