Chapter 13, Problem 18RE

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Find the velocity, speed, and acceleration of a particle moving with position function **r**(*t*) = (2*t*^{2} − 3) **i** + 2*t* **j**. Sketch the path of the particle and draw the position, velocity, and acceleration vectors for *t* = 1.

To determine

**To find:** The velocity of a particle that moves with the position function

Explanation

**Given data:**

The particle moves with the position function

**Formula used:**

Write the expression to find the velocity with the position function

Write the required differentiation formulae to obtain the solution as follows.

Write the expression to find the speed of a particle with the position function

Write the expression to find the acceleration of a particle with the position function

Here,

Substitute

Simplify the expression as follows.

Thus, the velocity of a particle that moves with the position function

**Calculation of speed of a particle:**

Substitute

Thus, the speed of a particle that moves with the position function

Sect-13.1 P-1ESect-13.1 P-2ESect-13.1 P-3ESect-13.1 P-4ESect-13.1 P-5ESect-13.1 P-6ESect-13.1 P-7ESect-13.1 P-8ESect-13.1 P-9ESect-13.1 P-10E

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