Chapter 1.4, Problem 2aT

On a separate part of your paper, copy the velocity vectors $\stackrel{\to }{{\upsilon }_C}\text{and}\stackrel{\to }{{\upsilon }_D}$ . From these vectors, determine the change in velocity vector, $\Delta \stackrel{\to }{\upsilon }$ .

1. Is the angle formed by the "head" of $\stackrel{\to }{{\upsilon }_c}$ and the "tail" of $\Delta \stackrel{\to }{\upsilon }$ greater than, less than, or equal to $90°$ ?

As point D is chosen to lie closer to point C, does the above angle increase, decrease, or remain the same? Explain how you can tell.

Does the above angle approach a limiting value? If so, what is its limiting value?

2. Describe how to use the change in velocity vector to determine the average acceleration of the object between C and D. Draw a vector to represent the average acceleration between points C and D.

What happens to the magnitude of $\Delta \stackrel{\to }{\upsilon }$ as point D is chosen and closer to point C? Does the acceleration change in the same way? Explain.

Consider the direction of the acceleration at point C. Is the angle between the acceleration vector and the velocity vector greater than, less than, or equal to $90°$ ? (Note: Conventionally, the angle between two vectors is defined as the angle formed when they are placed "tail-to-tail".)