Chapter 4.3, Problem 100E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Motion Along a Line In Exercises 97-100, the function s(f) describes the motion of a particle along a line, (a) Find the velocity function of the particle at any time t ≥ 0 . (b) Identify the time interval(s) on which the particle is moving in a positive direction, (c) Identify the time inters al(s) on which the particle is moving in a negative direction, (d) Identify the time(s) at which the particle changes direction. s ( t ) = t 3 − 20 t 2 + 128 t − 280

(a)

To determine

To calculate: The velocity function for the particle if s(t)=t320t2+128t280.

Explanation

Given:

The distance function is s(t)=t3âˆ’20t2+128tâˆ’280

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))=ddt

(b)

To determine

To calculate: The interval where the particle is moving in the positive direction if s(t)=t320t2+128t280.

(c)

To determine

To calculate: The interval where the particle is moving in the negative direction if s(t)=t320t2+128t280.

(d)

To determine

To calculate: The time when the direction of the particle changes if s(t)=t320t2+128t280.

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