Question

In Exercises 23-26, a solution curve in the xy-plane and an initial condition on that curve are specified. Sketch the x(t) - and y(t)-graphs for the solution. 24.

Answer 1

To sketch x(t) and y(t) graphs, one must find the tangent line at a specific point, determine endpoints related to the tangent to find the slope, and use this slope to illustrate the relation between the solution curve and the x(t) and y(t) graphs.

Step-by-step explanation:

The student is asked to sketch the x(t) and y(t) graphs for a given solution curve in the xy-plane and an initial condition on that curve. To do this, one would typically need the specific equation representing the curve and the initial condition. However, as there isn't a specific equation given in the question, let's use an example process.

1. Find the tangent line to the curve at a specific time, such as t = 25 s.
2. Determine the endpoints of the tangent, which will correspond to specific positions at given times.
3. Use these endpoints to solve for the slope, which represents the velocity in the context of motion.

The slope of the x(t) graph at any point is the instantaneous velocity at that point. This is shown as the slope of the tangent line to the curve at that specific time. The velocity-versus-time graph can be used to sketch the position-versus-time graph by integrating the velocity curve over time to get the position.