Unit: Particle Moving with Constant Velocity

Instructional goals

By the end of this unit, you should be able to do the following:

1. You should be able to determine the average velocity of an object in two ways:

- by determining the slope of an x vs. t graph.       
- by using the equation V = ▲x/▲t = displacement/time.

2. You should be able to determine the displacement of an object in two ways:

- by finding the area under a v vs. t graph.
- by using the equation ▲x=vt.

3. Given an x vs. t graph

- describe the motion of the object (starting position, direction of motion, velocity).
- draw the corresponding v vs. t graph.
- draw a motion map for the object.
- determine the average velocity of the object (from the slope).
- write the mathematical representation that describes the motion.

4. Given a v vs. t graph,

-describe the motion of the object (direction of motion, how fast).
-draw the corresponding x vs. t graph.
-determine the displacement of the object (from the area under curve).
-draw a motion map for the object.
-write a mathematical representation to describe the motion.

Terms and Definitions:

Average Velocity = Slope of x-t graph = change in position/change in time =▲x/▲t = x_f - x_{i /Tf - Ti} 

▲x = change in position = x_f - x_i = displacement = area under v-t graph. Displacement is the straight-line distance between the initial and final positions. Displacement is a vector; thus it conveys information about the direction of motion.

Path length = total distance traveled along a path to move from the starting position to the ending position.

Average Speed = path length / change in time

Scalar = A quantity that tells magnitude (how much); i.e., speed, time, mass, odometer reading . . .

Vector = A quantity that tells both magnitude and direction; i.e., velocity, displacement, force . . .

Qualitative = Conceptually correct, but not numerically precise

Quantitative = Numerically Accurate