Gold: Important concept. Very likely to appear on an assessment. Notes:Color Guide Gold: Important concept. Very likely to appear on an assessment. Blue: Supplemental information. Will not directly appear on an assessment. Red: Example. Copy if needed. White: Will be discussed by Mr. Williams.

Chapter 2: Motion in One Dimension Section 1: Displacement & Velocity

Motion is the change of an object’s position relative to some reference point. In order to distinguish motion, a frame of reference must be used. The signal light, power line poles, and hills can be used as a frame of reference.

Displacement: ∆x = xf – xi Objects that are “at rest” are not in motion. When an object changes its position, it becomes displaced. The displacement measures how far an object has moved from it’s starting position. Note: ∆ is the Greek symbol “delta”. It means “a change in”. xf means final position. xi means initial position. Displacement: ∆x = xf – xi

The displacement of an object does not always equal the distance it has traveled.

Displacement can be either positive or negative…depending on your frame of reference. The right (or east) will be considered positive unless otherwise stated. Likewise with up (north). The left (or west) will be considered negative unless otherwise stated. Likewise with down (south). ∆x = -4 cm ∆x = 8 cm Negative Positive

With your partner, discuss the following: What is this object’s position at 1 minute? What is the object’s position at 2 minutes? What is its displacement between 1 min and 5 min? Describe the motion of this object.

Velocity: v = ∆x = (xf-xi) Displacment is only one portion of an object’s motion. What if we also consider how long it took the object to change it’s position? Average velocity is the total displacement divided by the total amount of time during the displacement. Velocity may be + or - , depending on the displacement. Velocity: v = ∆x = (xf-xi) ∆t (tf – ti)

Why refer to it as average velocity? Example: Suppose you traveled from your house to school…a distance of 4.0 km. It took you .20 hours (12 minutes) because of heavy traffic. Your avg velocity would be: v = 4.0 km / .20 h v = 20 km/h Did you travel at that exact speed for the entire trip? Of course not. Because of this, velocity is an average.

Velocity and Speed are often used interchangeably. Velocity and speed are not the same: Velocity requires some direction. Speed refers to the numerical value (magnitude) of velocity.

(Final) Position: xf = v∆t + xi Using the velocity equation, we can derive another equation to find an object’s position With your partner… 1) Use the base velocity equation to derive an equation to solve for the final position of an object. (Final) Position: xf = v∆t + xi

The slope of a position-time graph gives the velocity. Velocity can be determined using a position vs time graph. The slope of a position-time graph gives the velocity.

Position vs Time How could we describe the motion of these objects?

Chapter 2: Motion in One Dimension Section 2: Accelerated Motion

Acceleration: a = ∆v/∆t = vf - vi Objects accelerate when they change their motion – either speed or directions (or both). Specifically, the change in velocity over time. An object accelerates when it changes its motion. This means: Speeding up Slowing down Changing direction Acceleration: a = ∆v/∆t = vf - vi tf - ti

An object only accelerates when it experiences UNBALANCED forces. The net force acting on an accelerating object is NOT zero! The net force and the acceleration must have the same sign.

The standard unit for acceleration is m/s/s. It is often written as m/s2 . With your partner… Use the acceleration formula to show how the unit of m/s2 is obtained. Explain, in plain speak, what the unit m/s2 means. m 1 s s x = _m_ s x s s2 m _s_ s

Velocity vs Time The slope of a velocity vs time graph represents acceleration.

The acceleration is constant and downward. Falling Objects Free fall is a state of motion in which gravity is the only force affecting the object. The acceleration is constant and downward.

All objects free fall with an acceleration of -9.8 m/s/s. In other words, gravity causes objects to speed up as they fall downward. In our studies, we will usually neglect air resistance until FRICTION is covered in more detail.

Dropped from some height. For any object that is: Dropped from some height. Thrown upward. Thrown horizontally. The acceleration is ALWAYS downward and constant at -9.8 m/s/s.

Each of these objects is in free fall. The velocity vs. time graph for any object in free fall has a negative slope.

We now have all the tools necessary to explore the Kinematic Equations. The Kinematic Equations describe the mathematical relationships that exist between an object’s motion. Displacement Velocity Acceleration Time

vf = vi + a∆t Note that: Velocity with Constant Acceleration: This equation does not require displacement. ∆t = (tf – ti) vf = vi + a∆t

vf2 = vi2 + 2a∆x Note that: Velocity with Constant Acceleration: This equation does not require time. ∆x = (xf – xi) vf2 = vi2 + 2a∆x

∆x = vit + ½at2 Note that: “t” is actually “∆t”. Displacement with Constant Acceleration: Note that: “t” is actually “∆t”. However, ti is usually 0. ∆x = vit + ½at2

vf + vi 2 ∆x = t Note that: Displacement with Constant Acceleration: This equation does not require acceleration. vf + vi 2 ∆x = t