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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem
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Finding Velocity and Acceleration Vectors in Space In Exercises 37-40, the position vector r describes the path of an object Moving in space. (a) Find the velocity vector, speed, and acceleration vector of the object. (b) Evaluate the velocity vector and acceleration vector of the object at the given value of t.

Position Vector Time

r ( t ) = 4 t i + t 3 j t k

t = 1

(a)

To determine

To calculate: The velocity vector, speed and acceleration vector of the object where, the displacement vector is r(t)=4ti+t3jtk.

Explanation

Given:

The vector is: r(t)=4ti+t3jtk, t=1.

Formula used:

The velocity is v(t)=d(r)dx where v(t) is the velocity vector.

Magnitude of a vector v=ai+bj is v=a2+b2.

The acceleration of a vector is a(t)=ddt(v(t)) where v(t) is the velocity vector and a(t) is the acceleration vector.

Calculation:

Consider the vector,

r(t)=4ti+t3jtk

The vector velocity is

v(t)=d(r)dx=4i

(b)

To determine

To calculate: The velocity vector and acceleration vector of the object r(t)=4ti+t3jtk when t=1.

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