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A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a certain point P with an initial velocity of 4 ft/s. Another particle is also moving along the same path which starts at a distance of 3 ft to the left of P with an initial velocity of 8 ft/s. Suppose the acceleration of the two particles are given by a1 (t) = 2t – 3 and a2(t) = 2t – 5, respectively. Will the two particles collide? Justify your answer.

A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a certain point P with an initial velocity of 4 ft/s. Another particle is also moving along the same path which starts at a distance of 3 ft to the left of P with an initial velocity of 8 ft/s. Suppose the acceleration of the two particles are given by a1 (t) = 2t – 3 and a2(t) = 2t – 5, respectively. Will the two particles collide? Justify your answer.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please answer this question using the Particular Antiderivatives: Application to Rectilinear Motion.

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A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a certain point P with an initial velocity of 4 ft/s. Another particle is also moving along the same path which starts at a distance of 3 ft to the left of P with an initial velocity of 8 ft/s. Suppose the acceleration of the two particles are given by a1 (t) = 2t – 3 and a2(t) = 2t – 5, respectively. Will the two particles collide? Justify your answer.
Transcribed Image Text:A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a certain point P with an initial velocity of 4 ft/s. Another particle is also moving along the same path which starts at a distance of 3 ft to the left of P with an initial velocity of 8 ft/s. Suppose the acceleration of the two particles are given by a1 (t) = 2t – 3 and a2(t) = 2t – 5, respectively. Will the two particles collide? Justify your answer.
Rectilinear Motion Revisited Suppose a particle is moving along a line and its equation of motion is given by s(t). If v(t) and a(t) are the equations of velocity and acceleration, respectively, of the particle, then v(t) = s'(t) and a(t) = v'(t). s(t) is a particular antiderivative of v(t) v(t) is a particular antiderivative of a(t) Example A heavy projectile is fired straight up from a platform 3 meters above the ground with an initial velocity of 160 m/s. Find an equation of motion of the particle. (Use -10 m/s2 for acceleration due to gravity.) a(t) -10 [(-10) đt v(t) -10t +C (1)a Initial Condition: v(0) = 160 160 -10 - 0+C %3D C 160 %3D Equation of velocity: v(t) = -10t +160 Example A heavy projectile is fired straight up from a platform 3 meters above the ground with an initial velocity of 160 m/s. Find an equation of motion of the particle. (Use -10 m/s? for acceleration due to gravity.) v (t) -10t + 160 s (t) -10t+160) dt s (t) - 512 + 160t +C Initial Condition: s(0) = 3 3 0 +0+C C 3 Equation of motion: s(t) -512 + 160t +3
Transcribed Image Text:Rectilinear Motion Revisited Suppose a particle is moving along a line and its equation of motion is given by s(t). If v(t) and a(t) are the equations of velocity and acceleration, respectively, of the particle, then v(t) = s'(t) and a(t) = v'(t). s(t) is a particular antiderivative of v(t) v(t) is a particular antiderivative of a(t) Example A heavy projectile is fired straight up from a platform 3 meters above the ground with an initial velocity of 160 m/s. Find an equation of motion of the particle. (Use -10 m/s2 for acceleration due to gravity.) a(t) -10 [(-10) đt v(t) -10t +C (1)a Initial Condition: v(0) = 160 160 -10 - 0+C %3D C 160 %3D Equation of velocity: v(t) = -10t +160 Example A heavy projectile is fired straight up from a platform 3 meters above the ground with an initial velocity of 160 m/s. Find an equation of motion of the particle. (Use -10 m/s? for acceleration due to gravity.) v (t) -10t + 160 s (t) -10t+160) dt s (t) - 512 + 160t +C Initial Condition: s(0) = 3 3 0 +0+C C 3 Equation of motion: s(t) -512 + 160t +3
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