Higher Order Derivatives Uses: acceleration, concavity Position: s (t) Second Derivative: Velocity: v (t) = s' (t) %3D d ( dy dæ ( dæ dy also f", y" dæ? Acceleration: a (t) = v' (t) = s" (t) 1. The height in feet at any time t (in seconds) of a particle thrown vertically is h (t) = –16t² + 256t. a. Find the particle's average velocity for the first 3 second of travel. b. How fast is the particle traveling 6 seconds after it is thrown and how high is it? c. When does the article reach its maximum height and what is that maximum height? d. What is the acceleration of the particle at t = 5 seconds?

Higher Order Derivatives Uses: acceleration, concavity Position: s (t) Second Derivative: Velocity: v (t) = s' (t) %3D d ( dy dæ ( dæ dy also f", y" dæ? Acceleration: a (t) = v' (t) = s" (t) 1. The height in feet at any time t (in seconds) of a particle thrown vertically is h (t) = –16t² + 256t. a. Find the particle's average velocity for the first 3 second of travel. b. How fast is the particle traveling 6 seconds after it is thrown and how high is it? c. When does the article reach its maximum height and what is that maximum height? d. What is the acceleration of the particle at t = 5 seconds?

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Higher Order Derivatives
Uses: acceleration, concavity
Position: s (t)
Second Derivative:
Velocity: v (t) = s' (t)
dy
also f", y"
dx?
d
dy
Acceleration: a (t) = v' (t) = s" (t)
dx
dx
1. The height in feet at any time t (in seconds) of a particle thrown vertically is h (t)
= -16t? + 256t.
a. Find the particle's average velocity for the first 3 second of travel.
b. How fast is the particle traveling 6 seconds after it is thrown and how high is it?
c. When does the article reach its maximum height and what is that maximum height?
d. What is the acceleration of the particle at t = 5 seconds?

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