1. Suppose that a particle moves according to the law of motion s(t) = 4, 20. (a) Find the velocity v(t) at time t. (b) Find all values of t for which the particle is at rest. (c) Use the interval notation to indicate when the particle is moving in the positive direction and when it is moving in the negative direction. (d) Find the total distance traveled during the first 5 seconds. 2. Newton's law of gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is F = GM, where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr (What does the minus sign mean?) (b) Suppose it is known that earth attracts an object with a force that decreases at a rate of 2N/km when r = 20000km? How fast does this force change when r = 10000km? 3. In the mysterious lost city of Mim, the length of daylight (in hours) on the tth day of the year is modeled by the function L(t) = 12+3 sin((-80)). Use this model to compare how the number of daylight is changing on March 19 and July 18? (assume that this is a standard year, not a leap year. Find the rate of changes in given days and then compare them).
1. Suppose that a particle moves according to the law of motion s(t) = 4, 20. (a) Find the velocity v(t) at time t. (b) Find all values of t for which the particle is at rest. (c) Use the interval notation to indicate when the particle is moving in the positive direction and when it is moving in the negative direction. (d) Find the total distance traveled during the first 5 seconds. 2. Newton's law of gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is F = GM, where G is the gravitational constant and r is the distance between the bodies. (a) Find dF/dr (What does the minus sign mean?) (b) Suppose it is known that earth attracts an object with a force that decreases at a rate of 2N/km when r = 20000km? How fast does this force change when r = 10000km? 3. In the mysterious lost city of Mim, the length of daylight (in hours) on the tth day of the year is modeled by the function L(t) = 12+3 sin((-80)). Use this model to compare how the number of daylight is changing on March 19 and July 18? (assume that this is a standard year, not a leap year. Find the rate of changes in given days and then compare them).
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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Transcribed Image Text:1. Suppose that a particle moves according to the law of motion s(t) = 4g, t≥ 0.
(a) Find the velocity v(t) at time t.
(b) Find all values of t for which the particle is at rest.
(c) Use the interval notation to indicate when the particle is moving in the positive direction and
when it is moving in the negative direction.
(d) Find the total distance traveled during the first 5 seconds.
2. Newton's law of gravitation says that the magnitude F of the force exerted by a body of mass m on
a body of mass M is F = GM, where G is the gravitational constant and r is the distance between
the bodies.
(a) Find dF/dr (What does the minus sign mean?)
(b) Suppose it is known that earth attracts an object with a force that decreases at a rate of 2N/km
when r = 20000km? How fast does this force change when r = 10000km?
3. In the mysterious lost city of Mim, the length of daylight (in hours) on the tth day of the year is
modeled by the function L(t) = 12 +3 sin((t-80)). Use this model to compare how the number of
daylight is changing on March 19 and July 18? (assume that this is a standard year, not a leap year.
Find the rate of changes in given days and then compare them).
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