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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 3.3, Problem 35E

(a)

To determine

**To find:** The velocity and acceleration at time *t.*

Expert Solution

The velocity of smooth level surface is

The acceleration of smooth level surface is

**Given:**

The equation of motion is *t* is in seconds and *x* is in centimeters.

**Derivative rule:**

Constant Multiple Rule:

If *c* is constant and

**Recall:**

If *x* is a displacement of a particle and the time *t* is in seconds, then the velocity of the particle is

If *t* is in seconds, then the acceleration of the particle is

**Calculation:**

Obtain the velocity at time *t.*

Apply the Constant Multiple Rule as shown in equation (1),

Thus, the velocity of

Obtain the acceleration at time *t.*

Apply the Constant Multiple Rule as shown in equation (1),

Therefore, the acceleration of

(b)

To determine

**To find:** The position, velocity and acceleration at

Expert Solution

The position, velocity and acceleration at

The direction of the particle is moving to the left (negative direction).

**Given:**

The equation of motion is *t* is in seconds and *x* is in centimeters.

**Calculation:**

The position

Thus, the position

From part (a), the velocity of

The velocity

Thus, the velocity

From part (a), the acceleration of

The acceleration

Thus, the acceleration

Here, the velocity of the particle at

This implies that, the velocity of the particle at

Therefore,the direction of the particle is moving to the left (negative direction).