   Chapter 4.4, Problem 95E

Chapter
Section
Textbook Problem

Particle Motion In Exercises 93-98, the velocity function, in feet per second, is given for a particle moving along a straight line, where t is the time in seconds. Find (a) the displacement and (b) the total distance that the particle travels over the given interval. v ( t ) = t 3 − 10 t 2 + 27 t − 18 ,       1 ≤ t ≤ 7

(a)

To determine

To calculate: The displacement of the car travelling in straight line with velocity function v(t)=t310t2+27t18 in the interval 1t7.

Explanation

Given:

The velocity function in feet per second, v(t)=t310t2+27t18 in the interval 1t7.

Formula used:

The displacement can be found by following the given formula,

Displacement=abv(t)dt

And,

xndx=xn+1n+1

Calculation:

Displacement=17(t310t2+27t18)dt=[t4410t33+27t2218t]17=[7<

(b)

To determine

To calculate: The distance of the car travelling in straight line with the velocity function v(t)=t310t2+27t18 in the interval 1t7.

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