Since this represents a maximum of the vertical position function for the pumpkin trajectory, y (x), find the maximum height the pumpkin reaches during its trajectory.

Consider an object moving along a line with the following velocity and initial position. vit) 9-t on (0,4) s0)= -4 Determine the position function for t20 using both the antiderivative method and …

The position function s (t) = t3-8t gives the position in miles of a freight train where east is the positive direction and t is measured in hours. a. Determine the direction the train is traveling in …

An object has a position function x (t) = 5t m. (a) What is the velocity as a function of time? (b) Graph the position function and the velocity function.

EXAMPLE 6 A particle moves in a straight line and has acceleration given by a (t) = 12t + 10. Its initial velocity is v (0) = -6 cm/s and its initial displacement is s (0) = 8 cm. Find its position …

The graph of the position function (the distance to the right of a fixed point as a function of time) is shown below. Answer the following questions only on the interval (0,8). 1,0 -1 Transcribed …

A mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position Xo and initial velocity Vo. …

A particle moves along a vertical coordinate axis so that its position at any time between 0 and 10 seconds is given by the position function below where s is measured in centimeters and t is …

In Problems 11 through 18, find the position function x (t) of a moving particle with the given acceleration a (t), initial posi- tion xo = x (0), and initial velocity vo = v (0).