   Chapter 4.R, Problem 46E

Chapter
Section
Textbook Problem

# A particle moves along a line with velocity function v ( t ) = t 2 − t , where v is measured in meters per second. Find (a) the displacement and (b) the distance travelled by the particle during the time interval [0, 5].

To determine

(a)

To find:

The displacement

Explanation

1) Concept:

i) The displacement of a particle is calculated by using the integrating velocity function that is t=vtdt

ii) ab[fx+gx] dx=abfxdx+abgxdx

iii) xmdx=xm+1m+1+C

2) Given:

vt=t2-t the velocity function measured in meter per second.

3) Calculation:

The given velocity of the particle is vt=t2-t

Therefore, the displacement of the particle can be calculated by using the formula

st=vtdt

st=(t2-t) dt

st=(t2) dt-t dt

Integrate using the property

s

To determine

(b)

To find:

The distance travelled by the particle during the time interval [0, 5]

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