CALCULUS WORKSHEET 1 ON PARTICLE MOTION Work these on W. Use your calculator only on part (f) of problems 1. Do not use your calculator on the other problems. Write your justifications in a sentence. 1. Aparticle moves along a horizontal line so that its position at any time is given by S [ t] = t3 12t2 + 35L f 2 0, where s is measured in meters and tin seconds. (a) Find the instantaneous velocity at time t and at t = 3 seconds. (b) When is the particle at rest? Moving to the right? Moving to the left? Justify your answers. (c) Find the displacement of the particle after the first 8 seconds. (d) Find the total distance traveled by the particle during the first 8 seconds. (e) Find the acceleration of the particle at time t and at t = 3 seconds. (f) Graph the position, velocity, and acceleration functions for 0 S t S 8 . (g) When is the particle speeding up? Slowing down? Justify your answers. 2. The maximum acceleration attained on the interval 0 S t S 3 by the particle whose velocity is given by v(t) =t33t2+12t+4 is (A) 9 (B) 12 (C) 14 (D) 21 (E) 40 3. The figure on the right shows the position 5 of a particle moving along a horizontal line. 5 {cm} (a) When is the particle moving to the left? moving to the right? standing still? Justify your answer. (b) For each of v{ 1.5) , v[ 2.5) , v[ 4}, and v[ 5) , nd the value or explain why it does not exist. (c) Graph the particle's velocity. (d) Graph the particle's speed. 4. (2005) A car is traveling on a straight road. For 05 t S 24 seconds, the car's velocity V\") , \"m "" 4. 20 HS. 20 in meters per second, is modeled by the E 2|} ( } I _' piecewise-linear function dened by the g 15 graph on the right. g :2." w (a) For each of V14] and $3120). nd the value E 5 or explain why it does not exist. Indicate 4 3 12 If 20 24 units of measure. Time {seconds} (b) Let a [ t} be the car's acceleration at time t, in meters per second per second. For 0