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d. e. -90++72) af At time = 2 is the particle moving to the right or to the left? Justify your result. v=S' (+) = 18€ Aft=2 √(2) = 18 (2) ²-90 (2) +72 The particle is moving 72-180+72 = -13 to the left at +=2 since the velocity ist Is the particle slowing down or speeding up. Justify your result. -19 (+) = v' (t) = 79(+) = 36€ -90 A++=2since the particle 9(2)=362-90. The left.

d. e. -90++72) af At time = 2 is the particle moving to the right or to the left? Justify your result. v=S' (+) = 18€ Aft=2 √(2) = 18 (2) ²-90 (2) +72 The particle is moving 72-180+72 = -13 to the left at +=2 since the velocity ist Is the particle slowing down or speeding up. Justify your result. -19 (+) = v' (t) = 79(+) = 36€ -90 A++=2since the particle 9(2)=362-90. The left.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer part d and e

8. a. C. 7. d. e. Find values of a and b that make the function below both continuous and differentiable at x =/ (ax+b, if x < 11 if x ≥ 11 f(x) = {0x²₁ on back 9(11)+b llab Let s(t) = 6t³ - 45t² + 72t be the equation of the position of a particle. Find a function for the velocity of the particle. b. √(+) = a (6+3_45€ ²+72€) v(+) = 18€²-90€ +72 When is the particle at rest? a particle is at rest 18€²_90€ +72=0 €²²-5++4=0 € ²-4+ - ++4=r the Find a function for the acceleration of the particle. 74 210=zabb 2a4D + b a=stan velocity function = v(+) = S(x) 72 bo wher Particle is at rest at t=1 second + (x-4)₂ (+-1) = ( + (x-4) - (+-4) = 0 and += 4 seconds t=4 a (+) = d (18t² -90 +€ +72) At time = 2 is the particle moving to the right or to the left? Justify your result. v=S'(+) => √(²²) = 18€ ²-90€ +172 partic= 72-180 +72 =-17 Aft=2 V(2) = 18 (2) ²-90 (2) +72 The particle is mains to the left at +=2 since the velocity ist Is the particle slowing down or speeding up. Justify your result. 9(+)= v' (t) = 79(+)=36€ -90 A++= 2since the particle 9(2)=362-90 the left a (186²-90€ +72) (9(+) = 36t -90 9
Transcribed Image Text:8. a. C. 7. d. e. Find values of a and b that make the function below both continuous and differentiable at x =/ (ax+b, if x < 11 if x ≥ 11 f(x) = {0x²₁ on back 9(11)+b llab Let s(t) = 6t³ - 45t² + 72t be the equation of the position of a particle. Find a function for the velocity of the particle. b. √(+) = a (6+3_45€ ²+72€) v(+) = 18€²-90€ +72 When is the particle at rest? a particle is at rest 18€²_90€ +72=0 €²²-5++4=0 € ²-4+ - ++4=r the Find a function for the acceleration of the particle. 74 210=zabb 2a4D + b a=stan velocity function = v(+) = S(x) 72 bo wher Particle is at rest at t=1 second + (x-4)₂ (+-1) = ( + (x-4) - (+-4) = 0 and += 4 seconds t=4 a (+) = d (18t² -90 +€ +72) At time = 2 is the particle moving to the right or to the left? Justify your result. v=S'(+) => √(²²) = 18€ ²-90€ +172 partic= 72-180 +72 =-17 Aft=2 V(2) = 18 (2) ²-90 (2) +72 The particle is mains to the left at +=2 since the velocity ist Is the particle slowing down or speeding up. Justify your result. 9(+)= v' (t) = 79(+)=36€ -90 A++= 2since the particle 9(2)=362-90 the left a (186²-90€ +72) (9(+) = 36t -90 9
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