How Do You Determine When Acceleration Is Zero in Particle Motion Calculations?

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SUMMARY

The discussion focuses on determining when the acceleration of a particle is zero in the context of a velocity function given by v(t) = 20 + 12t² - t³ for t > 0. The acceleration function is derived as a(t) = v'(t) = 24t - 3t². Setting the acceleration to zero results in the equation 24t - 3t² = 0, which simplifies to t(24 - 3t) = 0. The solution indicates that the acceleration is zero at t = 8 seconds.

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A GCE OL pastpaper question...

Can someone get over this for me please...thanx ie

The velocity, v m/s, of a particle P after t seconds is given by
v = 20 + 12*t[squared] - t[cubed] , t is larger than 0.

Calculate the value of t when the acceleration of P is 0.
 
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[tex]v(t)=20+12t^2-t^3,\;\;t>0[/tex]

[tex]We \;know:\,a(t)=v\prime(t)[/tex]

[tex]a(t)=24t-3t^2=0[/tex]

[tex]t=8\,(sec)[/tex]
 

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