Chapter 3, Problem 36RE

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

Chapter
Section

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
Textbook Problem

# Motion Along a Line In Exercises 35 and 46, the function s(t) describes the motion of a particle along a line. (a) Find the velocity function of the particle at any time t ≥ (b) Identify the time interval(s) on which the particle is moving in a positive direction. (c) Identify the time interval(s) on which the particle is moving in a negative direction. (d) Identify the time(s) at which the particle changes direction. s ( t ) = 6 t 3 − 8 t + 3

(a)

To determine

To calculate: The velocity function for the particle s(t)=6t38t+3.

Explanation

Given:

The distance function is s(t)=6t38t+3

Formula used:

The speed is the rate of change of the distance with respect to time.

This implies that the function for speed can be computed by differentiating the function for distance with respect to time.

Calculation:

Differentiate the function s(t) with respect to t to obtain:

ddt(s(t))=d

(b)

To determine

To calculate: The interval where the particle is moving in the positive direction, where s(t)=6t38t+3

(c)

To determine

To calculate: The interval where the particle is moving in the negative direction.

(d)

To determine

To calculate: The time when the direction of the particle changes.

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