A particle moves according to the law of motion 8 = + - 8+2, +>0, where t is measured in seconds and s in feet. (a) Find the average velocity over the interval [1, 3] ft Answer. (b) Find the velocity at time t. ft Answer. S (c) What is the velocity after 3 seconds? Answer. E (d) What is the acceleration after 5 seconds? Answer. E It (e) Fort > 0, when is the particle moving in the positive direction? Answer.The gure shows the velocity tuft) of a particle moving on a horizontal coordinate line, for t in the closed interval [I], III]. (You can elicit on the graph to enlarge the image. l Note: Answer the questions below using points: lists of points, intervals, or unions of intervals, whichever is appropriate. * Part 1: Particle moving forward or backward [a]: When does the particle move forward? AI'I SWEET: {b} Iv'v'hen does the particle move backward? A\" SWEET: | Part 2: Acceleration | | Part 3: {in the particle speed | A particle moves according to the law of motion _ 3 2 -. st 8t +411, tgs, where t is measured in seconds and s in feet. {a} Find the average velocitv over the interval [I]J 3] t Answer: , I i a {b} Find the velocitv at time t. t Answer: I i a {c} What is the velocitv after 3 seconds? i Answer: I i a {d} What is the acceleration after seconds? t Answer: 2 i 32 {e} For t \"a i]. when is the particle moving in the positive direction? Answer: I A particle moves according to the law of motion where t i5 measured \"1 SECONDS anti S in feet. {a} Find the average velocitv over the interval [21 4] t Answer: I i s {tr} Find the velocity at time t. t Answer: I i s {c} What is the velocitv after 1 seconds\"? t Answer: I i a {d} What is the acceleration after 1 seconds? t Answer: I i 32 {e} For t 1: , when is the particle moving in the negative direction? Answer: I A particle moves according to the law of motion 18 s=, t+4 t '93 G, where t i3 measured in SECONDS EII'ICI S in TEET. {a} Find the average velocitv over the interval [2, E] t Answer: 2 i s {is} Find the velocity at time t. t Answer: I i a {c} What is the velocityr after 2 seconds? t Answer: I i s {d} What is the acceleration after 2 seconds? t Answer: I i 32 {e} For t :3 , when is the particle moving in the negative direction? Answer: I The position function eta particle is given hv s=2t3Qt217t, trait}. where a is measured in meters and f in seconds. Find all values at t a I] for 1.vhich the particle is moving at a velocitv at T %. t: 23 If an arrow is shot straight award on some moon with a 1.reloeitj,r of 24 %. its height in meters after t seconds is given by sit] = 24: 6:2. [a] What is the 1.relooit}r of the arrow after 4 seoonos'? an Answer: I s [b] How long will it take for the arrow to return and hit the moon? Answer: I s {C} 1in"'l.iith what velooity will the arrow hit the moon\"? to Answer: I s A ball is thrown upward from the too of a building 35'] feet tall. The height CIT the hall i3 described by the function art} = 1ist2 + so: + as], where t is the time in seconds and it = I] corresponds to the moment the hall is thrown. {a} Determine for which i.ialue oft the hall reachesthe maximum height and determine this maximum height. t: I 3 Main: Height: 2 ft {in} Determine when the hall reaches the ground. t = E s {c} With what velocity does the heii hit the ground"? An swe r: I At time t seconds. the position of a hotly moving along the eaxis is s s a = [t 12: + 45:} m. [a] Find the acceleration of the hotly each time the yelocity is zero. Enter your answer as a list if necessary. Answer: 2 32 [o] Find the speed of the hotly each time the acceleration is zero. Enter your answer as a list if necessary. at Answer: I a [c] Find the total distance traveled by the body from t = [I to t = 4. Answer: 2 m Explorers on a planet with a thin atmosphere want to measure the acceleration of gravit}r at its surface. So thev use a spring gun to launch a ball bearing vertically,r upward from the surface with a launch velocitv of 25 %. If we denote pv g; the acceleration of gravitv in that planet. in 3": then the ball hearing will move following the formula 3(t] = 251? % t2. If the ball bearing reaches its maximum height 39 seconds after being launched, what is the value of g3\