A ball moves in a straight line has an acceleration of a(t) = 2t + 5. Find the position function of the ball if its initial velocity is -3 cm per second and it’s initial position is 12 cm.

Step-by-step explanation:

Relation between acceleration, velocity and position:

The velocity function is the integral of the acceleration function.

The position function is the integral of the velocity function.

Acceleration:

As given by the problem, the acceleration function is

Velocity:

In which K is the constant of integration, which is the initial velocity. So K = -3 and:

Position:

In which K, the constant of integration, is the initial position. Since it is 12:

explanation:

step-by-step explanation:

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative