Problem 5. [15 pts] A particle moves along a horizontal axis with velocity v(t) = 2t-t² +3 meters per second. Find the total distance traveled and the average velocity during the time interval 0 ≤t≤ 4. Simplify your answer and include the units.

4. Please help me answer this question we’ll calculate and explained. A stone is thrown from the top of a 200 m cliff. The height of the stone relative to the ground is represented by the formula (shown in the image). The time t is in seconds and the height h in meters. A) Calculates its initial speed (instant variation rate at 0s.). B) Calculates the average rate of change for the first two seconds. C) Calculates the rate of instantaneous change at 2 seconds. D) From the results obtained in a), b) and c), describe the displacement of the stone.

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10. Suppose a stone is dropped from the observation deck of the Space Needle in Seattle, 160 meters above the ground. How long will it take for the stone to hit the ground? (You will need to know that the acceleration of gravity is a = -9.8 meters per second?.)