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

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To determine when the acceleration of a particle is zero, the velocity function v(t) = 20 + 12t² - t³ is analyzed. The acceleration is found by taking the derivative of the velocity, resulting in a(t) = 24t - 3t². Setting the acceleration equal to zero leads to the equation 24t - 3t² = 0. Solving this equation reveals that the acceleration is zero at t = 8 seconds. This calculation is essential for understanding particle motion in physics.
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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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v(t)=20+12t^2-t^3,\;\;t>0

We \;know:\,a(t)=v\prime(t)

a(t)=24t-3t^2=0

t=8\,(sec)
 

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