We will have the following:
First, we remember that velocity is the change of position with respect to time and this can be seen as the derivative of the position; and that the acceleration is the change of velocity with respect to time and this can be seen as the derivative of the velocity or the second derivative of the position; so:
Then velocity will be:
And finally the acceleration will be:
And thus, when we examine the problem at t = 250s we will have that the acceleration will be 8 units of distance / s^2; this due to the fact that the second derivative is a constant.
When the life preserver is dropped from the helicopter, the only force acting on the object is the gravitational force. This modifies the equations of motion. Thus, the working equation is written below:
h = vt + 0.5gt²
where
v is the initial velocity
g is the acceleration due to gravity equal to 9.81 m/s²
h is the height of the fall
h = (1.46 m/s)(1.8 s) + 0.5(9.81 m/s²)(1.8 s)
h = 11.457 m
The surface of the table and brick may not match up perfectly. This means that friction may occur leading to the brick slowing down or some bit of heat resulting from the contact.