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)=³-9t² +24t (a) Find the velocity (in ft/s) at time t. v(t) = (b) What is the velocity (in ft/s) after 1 second? v(1) = ft/s t= ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (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. () Find the acceleration (in ft/s2) at time t. a(t) = ft/s² Find the acceleration (in ft/s2) after 1 second. a(1) = ft/s² (9) Graph the position, velocity, and acceleration functions for 0 sts 6.
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)=³-9t² +24t (a) Find the velocity (in ft/s) at time t. v(t) = (b) What is the velocity (in ft/s) after 1 second? v(1) = ft/s t= ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.) (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (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. () Find the acceleration (in ft/s2) at time t. a(t) = ft/s² Find the acceleration (in ft/s2) after 1 second. a(1) = ft/s² (9) Graph the position, velocity, and acceleration functions for 0 sts 6.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)=3-9t² + 24t
(a) Find the velocity (in ft/s) at time t.
v(t) =
ft/s
(b) What is the velocity (in ft/s) after 1 second?
v(1) =
ft/s
(c) When is the particle at rest? (Enter your answers as a comma-separated list.)
t=
(d) When is the particle moving in the positive direction? (Enter your answer using interval notation.)
(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.
(f) Find the acceleration (in ft/s2) at time t.
a(t) =
P/s²
Find the acceleration (in ft/s2) after 1 second.
a(1) =
ft/s²
(9) Graph the position, velocity, and acceleration functions for 0 st s 6.
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