How Do You Analyze Particle Motion Given a Position Function?

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To analyze the particle motion given the position function x = (8t^3 - 3t^2 + 5) m, the first step is to find the velocity by taking the derivative, resulting in vx = 24t^2 - 6t. Setting vx to zero helps identify the times when the particle is at rest. For acceleration, the second derivative of the position function is needed, which gives a = 48t - 6. The particle's position and acceleration can then be calculated at the identified times t1 and t2. Understanding the relationship between position, velocity, and acceleration through derivatives is crucial for solving the problem.
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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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