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

[lihinii]

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.

 

[janhaa]

$$v(t)=20+12t^2-t^3,\;\;t>0$$

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

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

$$t=8\,(sec)$$

 

[tacman]

To calculate the acceleration, we need to find the second derivative of the velocity function.
The second derivative is given by: a = 24 - 6t

To find when the acceleration is 0, we set the equation equal to 0 and solve for t.
0 = 24 - 6t
6t = 24
t = 24/6
t = 4

Therefore, when t is equal to 4 seconds, the acceleration of particle P is 0.