Motion Along a Line In Exercises 81-84, 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 ≥ 0 . (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 − t 2
Motion Along a Line In Exercises 81-84, 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 ≥ 0 . (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 − t 2
Solution Summary: The author explains how the velocity function for the particle can be computed by differentiating the distance function with respect to time.
Motion Along a Line In Exercises 81-84, 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
≥
0
. (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.
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
Find the indefinite integral by making a change of variables. (Remember the constant of integration.)
√(x+4)
4)√6-x dx
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