Question

The position of a moving particle as a function of time is given by:

x = (4 - 0.1t) sin(0.8t)
y = (4 - 0.1t)cos(0.8t)
z = 0.4t⁽³/²⁾
w = log (4 -0.1t²)
Plot these functions on a separate sub-windows, with the first two graphs being placed in the same window, and the others each one is in different window.
The graph must have the following:
a. A title that describes the graph.
b. A legend outside the graph window that describes the individual curves.
c. x and y axis labels that describe the independent and dependent variables and their units.

Answer 1

The position of a particle along the x-axis can be determined by setting the position function to zero, and displacement is found by the difference in position over a specified time interval.

Step-by-step explanation:

The position of a particle along the x-axis can be determined by setting the position function to zero, and displacement is found by the difference in position over a specified time interval.

To determine the position of a particle at various times, one can analyze the motion's equations. For instance, if the position of a particle moving along the x-axis is given by the function x(t) = 4.0 - 2.0t meters, we can find at what time the particle crosses the origin by setting x(t) equal to zero. This yields t = 2.0 seconds. Furthermore, to calculate the displacement between two points in time, we compute the difference in the particle's positions at these times. For t = 3.0 s, x(3.0) = 4.0 - 2.0(3.0) = -2.0 m, and for t = 6.0 s, x(6.0) = 4.0 - 2.0(6.0) = -8.0 m. Hence, the displacement from t = 3.0 s to t = 6.0 s is -8.0 m - (-2.0 m) = -6.0 m.