Particle changing direction

[jeflow]

I was givin the question, The acceleration of a particle moving along the x-axis at time t is given by a(t)=4t-12. If the velocity is 10 when t=0 and the position is 4 when t=0, then the particle is changing direction at?

Would I start by taking the antiderivative of the acceleration, because it is the derivative of the velocity which must be set equal to zero to find when a particle is changing direction?

 

[Unco]

Sounds like a good strategy.

Looks like they want to give its position at each of those times as well.

 

[Guest]

Yes, you should find the time when v(t)=0;
Hence, you should find v(t) first;

\(\displaystyle v(t)=\int{a(t)dt}=\int(4t-2)dt=2t^2-2t+10\)

And now we should find roots of the equation:
\(\displaystyle t^2-t+5=0\)
This equation hasn't roots, therefore the particle will never change the direction.

 

[Unco]

Continue as you were, Jetflow.