Linear Motion - Particle Displacement

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SUMMARY

The discussion focuses on analyzing the motion of a particle along the x-axis using the velocity function v(t) = 9 - t². The key tasks include determining when the particle is moving to the right, to the left, and when it is stopped, as well as calculating the particle's displacement and total distance traveled over the interval 0 ≤ t ≤ 6 seconds. The integration of the velocity function dx = (9 - t²) dt is essential for finding the displacement and identifying critical points where the velocity equals zero.

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The function v(t) = 9 - t2 is the velocity in m/sec for a particle moving along the x-axis, where t is measured in seconds (t is greater than or equal to 0). Use analytic methods to solve:

(a) When the particle is moving to the right, to the left, and stopped.
(b) The particles displacement for 0 <= t <= 6 (<= means "less than or equal to")
(c) The total distance the particle traveled for 0 <= t <= 6

I'm going to be honest, i have no idea how to even start on the problem. Any help would be greatly appreciated.
 
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v(t) = dx/dt = 9 - t^2.
So dx = (9-t^2)*dt.
Find the integration and equate it to zero. You will get t for which the displacement is zero.
 

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