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Unformatted text preview: Solution for Long-answer Homework 4 Motion problems, including some uniform acceleration Solution to Long-answer Homework Problem 4.1(null) Problem: You are babysitting a restless baby and decide to take him out of the house for a walk in his stroller. You put him in his stroller on the front porch of the house and then, starting from rest at point P , you walk away from the house in the positive direction, accelerating until you reach a constant walking speed of 1m / s at point Q and continue at that constant speed. While walking past point R , you notice he has fallen asleep and so you turn around at point S , 100 seconds after leaving P , and walk back at the same constant speed. As you approach the porch, you begin to slow down at Q , ending at rest at P , 220 seconds after the start of your walk. (a)Sketch the average acceleration vector over the time interval from the instant you notice the toddler has fallen asleep until you are back at P . Explain your reasoning. If the acceleration is zero, indicate that explicitly; if it is nonzero, determine its magnitude. (b)Sketch the average acceleration vector over the entire trip from the instant you leave home at P until you are back at P . Explain your reasoning. If the acceleration is zero, indicate that explicitly; if it is non-zero, determine its magnitude. P Q S R Position of Stroller x (m) 10 90 100 Solution to Part (a) At R : t i = 100s v i = +1m / s At P : t f = 220s v f = 0m / s v = v f- v i = 0m / s- (1m / s) =- 1m / s t = t f- t i = 220s- 100s = 120s a av = v t =- 1m / s 120s =- 8 . 3 10- 3 m / s 2 The negative sign indicates the vector is headed in the left direction; the magnitude | a av | = 8 . 3 10- 3 m / s 2 Average Acceleration Vector Grading Key: Part (a) 4 Points Solution to Part (b) 1 At P i : t i = 0s v i = 0m / s At P f : t f = 220s v f = 0m / s v = 0 a av = 0 a = 0 Average Acceleration Vector Grading Key: Part (b) 4 Points Total Points for Problem: 8 Points Solution to Long-answer Homework Problem 4.2(Plugging and Chugging) Problem: A car has an initial velocity of +20m / s at t = 0s . Its acceleration is a constant- 5 . 0m / s 2 . (a)What is the cars displacement and velocity at t = 3 . 0s ? (b)What is the cars displacement and velocity at t = 8 . 0s ? (c)At what instant is the cars velocity zero? Solution to Part (a) We can use the position equation (displacement variation) to find displacement at time t , x = v i t + 1 2 a ( t ) 2 = parenleftBig 20 m s parenrightBig (3s) + 1 2 parenleftBig- 5 m s 2 parenrightBig (3s) 2 = 60m- 22 . 5m = 37 . 5m We can then use the velocity function to find the velocity at time t , v f = v i + a t = 20 m s + parenleftBig- 5 m s parenrightBig (3s) = 20 m s- 15 m s = 5 m s Grading Key: Part (a) 2 Points Solution to Part (b) Same deal, different number, x = parenleftBig 20 m s parenrightBig (8s) + 1 2 parenleftBig- 5 m s 2 parenrightBig (8s) 2 = 160m- 160m = 0m v f = v i + a t = 20 m s + parenleftBig...
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