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Math / Mathematics for the International Student: Mathematics SL 3 / Chapter 17 / Problem 5

Mathematics for the International Student: Mathematics SL | 3rd Edition | ISBN: 9781921972089 | Authors: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa

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A particle moves in a straight line with displacement function s(t) = 12t 2t 3 1

Chapter 17, Problem 5

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QUESTION:

A particle moves in a straight line with displacement function s(t) = 12t 2t 3 1 centimetres where t is in seconds, t > 0. a Find velocity and acceleration functions for the particles motion. b Find the initial conditions and interpret their meaning. c Find the times and positions when the particle reverses direction. d At what times is the particles: i speed increasing ii velocity increasing?

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QUESTION:

A particle moves in a straight line with displacement function s(t) = 12t 2t 3 1 centimetres where t is in seconds, t > 0. a Find velocity and acceleration functions for the particles motion. b Find the initial conditions and interpret their meaning. c Find the times and positions when the particle reverses direction. d At what times is the particles: i speed increasing ii velocity increasing?

ANSWER:

Step 1 of 7

a) It is given that centimetres.

Find and by differentiating w. r. t. as shown below:

The velocity is .

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