How Do You Analyze Particle Motion Given a Position Function?

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SUMMARY

The discussion focuses on analyzing the motion of a particle described by the position function x = (8t^3 - 3t^2 + 5) m. Participants seek to determine when the velocity vx equals 0 m/s and to find the particle's position and acceleration at specific times t1 and t2. Key equations referenced include vx = dx/dt for velocity and a = dv/dt for acceleration. The problem emphasizes the need for differentiation due to the time-dependent nature of acceleration.

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Homework Statement


The position of a particle is given by the function x = ( 8t^3 - 3t^2 + 5) m, where t is in s.
(a) At what time or times does vx = 0 m/s?

(b) What are the particle's position and acceleration at t1?

What are the particle's position and acceleration at t2?

Homework Equations


v1 = v0 + at
x1 = x0 + v0 + (1/2)at^2
vx = dx/dt
a = dv/dt


The Attempt at a Solution


Quite honestly, I'm not sure where to begin with this problem. If someone could help me to start it that would be greatly appreciated, thanks!
 
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You know that v = dx/dt, and a = dv/dt. So for starters, take the derivatives.
 
spin360 said:
1.
v1 = v0 + at
x1 = x0 + v0 + (1/2)at^2



these are equation for constant acceleration. for your case acceleration is time dependent so can't use these
 

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