**a)**

The magnitude of the velocity remains constant only if:

1. a = 0

2. a is perpendicular to v. In this case, only the direction changes. The magnitude remains constant.

For instant 1 and 3, we'll use a tilted coordinate axis.

Each diagram below shows the velocity and acceleration for an object at a certain instant in time.

a. For each instant, state whether the object is speeding up, slowing down, or neither (e.g. moving with constant speed). Base your answers on what you have done in tutorial and problem 1.

b. The diagram at right illustrates how the acceleration at instant l can be treated as having two components: one parallel to the velocity (a_{||}) and one perpendicular to the velocity (a_{⊥}).

For each of the other instants, draw a diagram similar to the one given for instant l. Label the parallel and perpendicular components of the acceleration relative to the velocity. If either component is zero, state so explicitly.

c. For each of the instants l-4, compare your descriptions of the motion in part a with the components of the acceleration in part b. Then answer the following:

i. Give a general rule that describes how the component of the acceleration parallel to the velocity affects the motion of an object.

ii. Give a general rule that describes how the component of the acceleration perpendicular to the velocity affects the motion of an object.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Acceleration in 2D concept. You can view video lessons to learn Acceleration in 2D. Or if you need more Acceleration in 2D practice, you can also practice Acceleration in 2D practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Kozliak's class at University of North Dakota.