   Chapter 4.4, Problem 96E

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 − 8 t 2 + 15 t ,       0 ≤ t ≤ 5

(a)

To determine

To calculate: The displacement of the car travelling in straight line with velocity function v(t)=t38t2+15t in the interval 0t5.

Explanation

Given:

The velocity function in feet per second, v(t)=t38t2+15t in the interval 0t5.

Formula used:

The displacement can be found by following formula,

Displacement=abv(t)dt

And,

xndx=xn+1n+1

Calculation:

Displacement=05(t38t2+15t)dt=[t44

(b)

To determine

To calculate: The distance of the car travelling in straight line with the velocity function v(t)=t38t2+15t in the interval 0t5.

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