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.

its d. the first coordintaes are 10,32

step-by-step explanation: