Explanation Calculation: Consider the given acceleration function, a t = t + 1 − 2 j − e − 2 t k Differentiate the velocity vector given by v t = ∫ a t d t . v t = ∫ t + 1 − 2 j − e − 2 t k d t = ∫ t + 1 − 2 d t j − e − 2 t d t k = − 1 t + 1 j + 1 2 e − 2 t k + c Consider the above equation. v t = − 1 t + 1 j + 1 2 e − 2 t k + c â€¦â€¦ (1) It is given that v 0 = 3 i − j at t = 0 . Substitute v 0 = 3 i − j , where t = 0 into equation (1) to solve for c as, v 0 = − 1 0 + 1 j + 1 2 e − 2 0 k + c 3 i − j = − 1 j + 1 2 k + c 3 i − j = − j + 1 2 k + c c = 3 i − 1 2 k Substitute c = 3 i − 1 2 k into equation (1) as, v t = − 1 t + 1 j + 1 2 e − 2 t k + 3 i − 1 2 k = 3 i − 1 t + 1 j + 1 2 e − 2 t k − 1 2 k = 3 i − 1 t + 1 j + 1 2 e − 2 t − 1 k Differentiate the position vector given by r t = ∫ v t d t . r t = ∫ 3 i − 1 t + 1 j + 1 2 e − 2 t − 1 k d t = ∫ 3 d t i − 1 t + 1 d t j + ∫ 1 2 e − 2 t − 1 d t k = 3 t i − ln 1 + t j + 1 2 − e − 2 t 2 − t k + c 1 Consider the above equation

12th Edition

ISBN: 9781119778189

Author: Anton, Howard, Bivens, Irl C., Davis, Stephen

Publisher: WILEY

See similar textbooks

Question

Chapter 12.6, Problem 20ES

To determine

To calculate: The position and velocity vectors of the particle if at=t+1−2j−e−2tk , v0=3i−j ; r0=2k .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.6, Problem 19ES

Chapter 12.6, Problem 21ES

Students have asked these similar questions

Here is a region R in Quadrant I. y 2.0 T 1.5 1.0 0.5 0.0 + 55 0.0 0.5 1.0 1.5 2.0 X It is bounded by y = x¹/3, y = 1, and x = 0. We want to evaluate this double integral. ONLY ONE order of integration will work. Good luck! The dA =???

43–46. Directions of change Consider the following functions f and points P. Sketch the xy-plane showing P and the level curve through P. Indicate (as in Figure 15.52) the directions of maximum increase, maximum decrease, and no change for f. ■ 45. f(x, y) = x² + xy + y² + 7; P(−3, 3)

EX-let d'be ametric on a vector space X induced from a norm hx and d defind by a Slab)= {od (a, if a = b (a,b)+is ab Show that cannot be induced froman norm on X. 2) let à be trivel metric show that I cannot be induced from an norm on X- 3) let M be closed subspace of anormed spacex Construct the space X/Mas a normed space. 4) let Mix be vector space of 2x3 matrices on R write with Prove convex set and hyper Plane of M 5) show that every a finite dimension subspace of anormed space is closed.

Chapter 12 Solutions

Calculus: Early Transcendentals

Ch. 12.1 - Prob. 1QCE Ch. 12.1 - Describe the graph of rt=1+2t,1+3t.Ch. 12.1 - Prob. 3QCE Ch. 12.1 - Prob. 4QCE Ch. 12.1 - Prob. 1ES Ch. 12.1 - Find the domain of r(t) and the value of rt0. 2....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Prob. 5ES Ch. 12.1 - Prob. 6ES

Knowledge Booster

The position and velocity vectors of the particle if a t = t + 1 − 2 j − e − 2 t k , v 0 = 3 i − j ; r 0 = 2 k .

Solution Summary: The author calculates the position and velocity vectors of the particle based on the given acceleration function.

To calculate: The position and velocity vectors of the particle if at=t+1−2j−e−2tk , v0=3i−j ; r0=2k .

Want to see the full answer?

Chapter 12 Solutions