Problem 1. A ball is thrown straight up into the air from a height of 5 feet and at an initial speed of 20 feet/second. Let s(t) denote the vertical position of the ball (measured in feet), v(t) denote the velocity of the ball (measured in feet/second), and a(t) denote the acceleration of the ball (measured in feet/second?). From physics, we know that s'(t) = v(t) and v'(t) = a(t). The careful reader will notice you have also been given s(0) and v(0) already for this particular situation. you are told that the ball's acceleration is given by a(t) = -16, find an equation for the po- sition of the ball (that is, find s(t)). (Hint: you are finding a particular solution of a differential equation with two initial conditions, provided above). If

Problem 1. A ball is thrown straight up into the air from a height of 5 feet and at an initial speed of 20 feet/second. Let s(t) denote the vertical position of the ball (measured in feet), v(t) denote the velocity of the ball (measured in feet/second), and a(t) denote the acceleration of the ball (measured in feet/second?). From physics, we know that s'(t) = v(t) and v'(t) = a(t). The careful reader will notice you have also been given s(0) and v(0) already for this particular situation. you are told that the ball's acceleration is given by a(t) = -16, find an equation for the po- sition of the ball (that is, find s(t)). (Hint: you are finding a particular solution of a differential equation with two initial conditions, provided above). If

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Problem 1. A ball is thrown straight up into the air from a height of 5 feet and at an initial speed
of 20 feet/second. Let s(t) denote the vertical position of the ball (measured in feet), v(t) denote the
velocity of the ball (measured in feet/second), and a(t) denote the acceleration of the ball (measured
in feet/second?). From physics, we know that s'(t) = v(t) and v'(t) = a(t). The careful reader will
notice you have also been given s(0) and v(0) already for this particular situation.
If you are told that the ball's acceleration is given by a(t) = –16, find an equation for the po-
sition of the ball (that is, find s(t)). (Hint: you are finding a particular solution of a differential
equation with two initial conditions, provided above).

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