A particle moves along a horizontal line. Its position function is s(t) for t is greater than or equal to 0. For each problem, find the velocity function v(t) and the acceleration function a(t). 1. s(t) = -t^4 + 12t^3
2. s(t) = -t^4 + 8t^3

1) Velocity

Acceleration

2) Velocity

Acceleration

Step-by-step explanation:

From Physics we remember that velocity () and acceleration () are the first and second derivatives of the function position in time. That is:

1) Let , where . The functions velocity and aceleration are, respectively:

Velocity

Acceleration

2) Let , where . The functions velocity and acceleration are, respectively:

Velocity

Acceleration