Aparticle moves along the x-axis and its position at time t-seconds is found by x(t)=12 + 20t – 2t^2 find acceleration @ t=6. ( i put -4) at what time does the particle change direction ? explain. find the speed of the particle at t = 6 seconds. is it increasing or decreasing?

The acceleration of the particle is the second derivative of its position function:

The particle has constant acceleration and as you said, .

The particle changes direction when the sign of its velocity alternates between positive and negative, which means we can find any time this happens by solving for , then verifying that the sign of changes to either side of this value of .

We have and , so indeed the velocity changes sign at , so the particle's direction also changes at this point.

We already found that , and the speed is the magnitude of velocity, which means that the speed at is 4. The particle has constant acceleration, which means its speed will be increasing.

4.08%

step-by-step explanation:

its a straight line parallel to the time axis