The position of a rabbit along a straight tunnel as a function of time is plotte

Question

The position of a rabbit along a straight tunnel as a function of time is plotted below. a) What is instantaneous velocity at t = 10.0 s? (Round to 1 decimal place.) b) What is the average velocity between t = 25.0 s and t = 30.0 s? (Round to 1 decimal place.) A pitcher throws a ball directly upward with an initial speed of upsilon_0 = 11.3 m/s. You can assume the acceleration due to gravity g = 9.81 m/s^2. The ball is released h = 1.28 m above the ground and returns to the ground t_f seconds later a) Sketch the y(t) and v(t) curves from t = 0 to t = t_f clearly labeling initial position and velocity on their respective curves. b) How long does it take to reach its maximum height? c) What maximum height does it reach?

Explanation / Answer

a)Make a tangent line at t = 10 s to find the instantaneous velocity by its slope. This is the less steep of the two blue lines above. This line seems to have a slope of rise/run = 14 m/50 s = .28 m/s

b)From 25 to 30 the rabbit displaces from 8 m to 16 m (read from the graph), again in 5 seconds giving an average velocity of 8m/5 s = 1.6 m/s

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