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Calculus

when is the particle speeding up? When is the particle slowing down? Answer in interval notation.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

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Concept explainers

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.

Question

H) when is the particle speeding up? When is the particle slowing down? Answer in interval notation.

A graphing calculator is recommended.
A particle moves according to a law of motion s = f(t), t > 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.)
f(t) = t - 9t2 + 24t
(a) Find the velocity (in ft/s) at time t.
v(t) =
31 - 18t + 24
ft/s
(b) What is the velocity (in ft/s) after 1 second?
v(1)I= 11
ft/s
(c) When is the particle at rest? (Enter your answers as a comma-separated list.)
t = 0
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
-10
(e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds.

(e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds.
ft
(f) Find the acceleration (in ft/s) at time t.
a(t) =
ft/s?
Find the acceleration (in ft/s) after 1 second.
a(1) =
ft/s2
(g) Graph the position, velocity, and acceleration functions for 0 sts6.
30
30
20
20
10
10

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