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1. The position of a particle for t> 0 is given by 7 (t) = ((3.1ť²) Î + (−6.6 t³) ĵ + (−4.7 t¯²) k) m. Assume all quantities are correct to 2 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? v(t)=(6.2t i+ -13.22² a(t) = (6.2 +-26.4t j+ -9.4t (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? (c) What is the particle's velocity at t = 2.2 s? m + -28.2t S m

1. The position of a particle for t> 0 is given by 7 (t) = ((3.1ť²) Î + (−6.6 t³) ĵ + (−4.7 t¯²) k) m. Assume all quantities are correct to 2 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? v(t)=(6.2t i+ -13.22² a(t) = (6.2 +-26.4t j+ -9.4t (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? (c) What is the particle's velocity at t = 2.2 s? m + -28.2t S m

Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter3: Vectors
Section: Chapter Questions
Problem 3.62AP: After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of...
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3-D Motion in relation to 2D/3D Kinematics

Homework: Three-Dimensional Motion 1. The position of a particle for t> 0 is given by 7(t) = ((3.1t²) Î + (−6.6 t³) ĵ + (−4.7 t¯²) k) m. Assume all quantities are correct to 2 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? ✓(t) = (6.2t m i+ -13.2² √√i+ −9.4t¯³√k) S (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? a(t) = (6.2 i+-26.4t (c) What is the particle's velocity at t = 2.2 s? √j+-28.2t¯¯ √k) m s²
Transcribed Image Text:Homework: Three-Dimensional Motion 1. The position of a particle for t> 0 is given by 7(t) = ((3.1t²) Î + (−6.6 t³) ĵ + (−4.7 t¯²) k) m. Assume all quantities are correct to 2 significant figures. (a) What is the velocity as a function of time t? Think: In terms of derivatives, how is velocity related to the postion vector when expressed as a function of time? ✓(t) = (6.2t m i+ -13.2² √√i+ −9.4t¯³√k) S (b) What is the acceleration as a function of time 't'? Think: In terms of derivatives, how is acceleration related to the velocity vector when expressed as a function of time? a(t) = (6.2 i+-26.4t (c) What is the particle's velocity at t = 2.2 s? √j+-28.2t¯¯ √k) m s²
Tunction of Lime? a(t) = (6.2 (c) What is the particle's velocity at t = 2.2 s? Enter to 2 significant figures v(t 2.2 s) (12 = |v(t=3 s) = 1.21x10² i+-26.4t v=( (d) What is its speed at t = 1.3 s and t = 3 s? Think: Speed at any instant is the magntitude of instantaneous velocity Enter to 2 significant figures |v(t=1.3 s) = 23 i+ m +-64 S m S +-28.2t ✔k) (e) What is the average velocity between t = 1.3 s and t = 3 s? Enter to 2 significant figures Think: What is the formula for the average velocity? X +-0.88 X m s² X m S m S
Transcribed Image Text:Tunction of Lime? a(t) = (6.2 (c) What is the particle's velocity at t = 2.2 s? Enter to 2 significant figures v(t 2.2 s) (12 = |v(t=3 s) = 1.21x10² i+-26.4t v=( (d) What is its speed at t = 1.3 s and t = 3 s? Think: Speed at any instant is the magntitude of instantaneous velocity Enter to 2 significant figures |v(t=1.3 s) = 23 i+ m +-64 S m S +-28.2t ✔k) (e) What is the average velocity between t = 1.3 s and t = 3 s? Enter to 2 significant figures Think: What is the formula for the average velocity? X +-0.88 X m s² X m S m S
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Tunction of Lime? a(t) = (6.2 (c) What is the particle's velocity at t = 2.2 s? Enter to 2 significant figures v(t 2.2 s) (12 = |v(t=3 s) = 1.21x10² i+-26.4t v=( (d) What is its speed at t = 1.3 s and t = 3 s? Think: Speed at any instant is the magntitude of instantaneous velocity Enter to 2 significant figures |v(t=1.3 s) = 23 i+ m +-64 S m S +-28.2t ✔k) (e) What is the average velocity between t = 1.3 s and t = 3 s? Enter to 2 significant figures Think: What is the formula for the average velocity? X +-0.88 X m s² X m S m S
Transcribed Image Text:Tunction of Lime? a(t) = (6.2 (c) What is the particle's velocity at t = 2.2 s? Enter to 2 significant figures v(t 2.2 s) (12 = |v(t=3 s) = 1.21x10² i+-26.4t v=( (d) What is its speed at t = 1.3 s and t = 3 s? Think: Speed at any instant is the magntitude of instantaneous velocity Enter to 2 significant figures |v(t=1.3 s) = 23 i+ m +-64 S m S +-28.2t ✔k) (e) What is the average velocity between t = 1.3 s and t = 3 s? Enter to 2 significant figures Think: What is the formula for the average velocity? X +-0.88 X m s² X m S m S
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