# Physics Unit 2 - Constant Velocity Particle Model

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Physics Classroom on Kinematics (esp. Lessons 2-4, 6)

Unit 2, Constant Velocity Model Concepts

By Marc Reif

The paradigm ("pattern") for this unit is the buggy. We observed the buggy traveling in a straight line (mostly), and covering equal amounts of distance in equal times. Upon examination of the motion of the buggy, we described it as constant velocity.

In order to measure lengths or positions, we must pick a reference point. Once we've picked a reference point, we generally call it "zero," and define to the left of the reference point as the negative direction (negative positions) and to the right of the reference point as the positive direction (positive positions).

Displacement (written "delta pos") is the change in position from a reference point. Displacement is a vector, meaning it has a magnitude (size) and a direction (often simply positive or negative).

Distance is how far you travel. It is a scalar because it has only a size, no direction. It is of less use in accurate descriptions of motion, so in physics we concentrate on displacement.

What we commonly call time can be described in two ways, a clock reading (you note what time the clock displays for an instant), and a time interval (delta t, or final time-initial time). How long does 12 noon last?

An instant is an infinitesimally small amount of time. It is the amount of time that passes in a clock reading.

An object can cover distance while ending up without displacement, if it returns to its starting point at the end of the time interval.

Average Speed is defined as total distance over total time. It is a scalar.

Average Velocity (v with a "bar" over it) is defined as the displacement (delta position) over the change in time (delta t). It is a vector because displacement is a vector. Thus it has a magnitude and a direction. A shorthand version of this definition is v = delta pos/delta t. The triple lines in the equality symbol denote a definition.

Instantaneous velocity is the velocity at an instant. Instantaneous speed is what your car's speedometer shows.

An object with constant velocity (the buggy, for example), always has an average velocity equal to its instantaneous velocity.

The velocity is the slope of a linear pos-t graph. If the velocity is constant, the pos-t graph must be linear ( it has one slope/velocity).

A linear pos-t graph can be modeled with an equation of the form y=mx + b

The intercept of the pos-t graph represents the initial velocity.

A linear pos-t graph implies a constant velocity-time graph (v-t graph). A constant graph is a horizontal line.

The area of a vel-t graph is the displacement.

The vel-t graph does not tell us anything about starting and ending positions, only about displacement.

19 April 2005