Explanation Given Info : Acceleration a ( t ) = t k Initial velocity v ( 0 ) = 1 i Initial position r ( 0 ) = 1 j Formula Used: (i) Apply the formula for velocity vector v ( t ) = ∫ a ( t ) d t + C 1 (iii) Apply the formula for position vector r ( t ) = ∫ v ( t ) d t + C 2 Here, all alphabets are in their usual meanings. Calculation: Apply the formula for velocity v ( t ) = ∫ a ( t ) d t + C 1 v ( t ) = ∫ t k d t + C 1 v ( t ) = t 2 2 k + C 1 − − − − − ( i ) Now, we shall apply given condition for initial velocity vector in equation (i) to calculated the integral constant ‘C 1 ’ 1 i + 0 j + 0 k = v ( 0 ) = 0 i + 0 j + 0 k + C 1 o r , C 1 = 1 i − − − − − − ( i i ) From equation (i) and (ii), the required expression for velocity vector v ( t ) can be calculated as v ( t ) = t 2 2 k + ( 1 i ) v ( t ) = 1 i + 0 j + t 2 2 k − − − − ( a ) v ( t ) = ( 1 , 0 , t 2 2 ) Apply ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 14.5, Problem 17E

To determine

To calculate position vector $r (t)$ and velocity $v (t)$ from the given conditions.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 16E

Chapter 14.5, Problem 18E

Students have asked these similar questions

O să vă imaginea și date compune o problemă 42 31 1 0 9

Find the largest interval centered about x = 0 for which the given initial value problem has a unique solution. y" + (tan x)y = ex, y(0) = 1, y'(0) = 0

1 L'Ina (ln x) 2020 dx 0

Chapter 14 Solutions

CALCULUS (CLOTH)

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To calculate position vector r ( t ) and velocity v ( t ) from the given conditions.

Solution Summary: The author explains how to calculate position vector r ( t ) and velocity v from the given conditions.

Concept explainers

Videos

To calculate position vector $r (t)$ and velocity $v (t)$ from the given conditions.

Want to see the full answer?

Chapter 14 Solutions

To calculate position vector r ( t ) and velocity v ( t ) from the given conditions.

Solution Summary: The author explains how to calculate position vector r ( t ) and velocity v from the given conditions.

Concept explainers

Videos

To calculate position vector r(t) and velocity v(t) from the given conditions.

Want to see the full answer?

Chapter 14 Solutions

To calculate position vector $r (t)$ and velocity $v (t)$ from the given conditions.