Speed and distance with vectors
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Speed and distance with vectors

[From: ] [author: ] [Date: 11-09-06] [Hit: ]
c) What is his speed when t = 1/(omega)?d) How far is he from the origin when t = 1/(omega)?Could someone help me with this problem, please? Id appreciate it!therefore,......
"An ant is crawling on a horizontal flat table's surface. In polar coordinates, his coordinates are r(t) = bt^2 and theta(t) = (omega)t where b and omega are known constants.

a) Find his velocity function v(t) in terms of t, b, omega and the polar unit vectors r-hat and theta-hat.

b) Find his acceleration vector a(t) in terms of t, b, omega and the polar units r-hat and theta-hat.

c) What is his speed when t = 1/(omega)?

d) How far is he from the origin when t = 1/(omega)?"

Could someone help me with this problem, please? I'd appreciate it!

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look in your book to find that the expression for velocity in polar coords is

v(t)= r dot r hat + r theta dot theta hat

where dot means derivative with respect to time

therefore, v(t)=2bt r hat + bt^2* omega theta hat

the expression for acceleration is a bit more complex

a(t)=(r double dot - r theta dot squared) r hat + (2 r dot theta dot + r theta double dot)theta hat

where double dot means the second time derivative

use the expressions for r(t) and theta(t) and solve for acceleration
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