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10th Edition

Ron Larson + 1 other

ISBN: 9781285057095

Textbook Problem

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Motion Along an Involute of a Circle The figure shows a particle moving along a path modeled by

The figure also shows the vectors v(t) and a(t) for

(a) Find

(b) Determine whether the speed of the particle is increasing or decreasing at each of the indicated values of t. Give reasons for your answers.

**(a)**

To determine

**To Calculate:** The value of the tangential and normal components of acceleration as,

Explanation

**Given:**

The provided position vector is,

**Formula Used:**

The tangential velocity and tangential acceleration are:

**Calculation:**

The velocity is calculated as shown below,

Now, find the magnitude of the velocity vector to find speed of the particle as shown below,

Now, find the acceleration vector of the particle as calculated below,

Now, find the tangential component of acceleration as shown below,

Since,

The value is found as shown below,

At

**(b)**

To determine

Whether the speed of particle is increasing or decreasing at each of the indicated value of *t* from t = 1 to t = 2 if the position vector is,

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