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[SOLVED] Calculus Problem - Maximum Velocity, Derivatives, etc.
A particle moves along a line so that at any time t its position given by x(t)=2[tex]\Pi[/tex]t + cos2[tex]\Pi[/tex]t.
What is the maximum velocity?
We found:
v(t) = 2[tex]\Pi[/tex] - sin2t[tex]\Pi[/tex](2[tex]\Pi[/tex])
a(t) = 2[tex]\Pi[/tex](-cos2t*[tex]\Pi[/tex])(2[tex]\Pi[/tex])
all values of t when particle's at rest in [0,3]: t=1/4, 5/4, 9/4
We tried setting the acceleration to zero and got t = 1/4, and plugged that into the velocity and got v(t) = 0, which makes no sense because the max velocity is not when it is at rest.
Any help would be GREATLY appreciated ... I have been working at this for 6 hours and am afraid that I am slowly withering away
Homework Statement
A particle moves along a line so that at any time t its position given by x(t)=2[tex]\Pi[/tex]t + cos2[tex]\Pi[/tex]t.
What is the maximum velocity?
Homework Equations
We found:
v(t) = 2[tex]\Pi[/tex] - sin2t[tex]\Pi[/tex](2[tex]\Pi[/tex])
a(t) = 2[tex]\Pi[/tex](-cos2t*[tex]\Pi[/tex])(2[tex]\Pi[/tex])
all values of t when particle's at rest in [0,3]: t=1/4, 5/4, 9/4
The Attempt at a Solution
We tried setting the acceleration to zero and got t = 1/4, and plugged that into the velocity and got v(t) = 0, which makes no sense because the max velocity is not when it is at rest.
Any help would be GREATLY appreciated ... I have been working at this for 6 hours and am afraid that I am slowly withering away
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