Ch+2+-+Motion+in+1D

**Motion in 1 Dimension ([|Syllabus])**
**BIG IDEA!!!** Listen to hear the BIG IDEA of this chapter. media type="file" key="big idea.mp3"

**Goals:** Understanding the relationships between distance, velocity, and acceleration

All Motion is Relative and depends on Frame of Refrence.

__Kinematics__- study of motion without regard for cause of motion. __Dynamics__- study of causes of motion (force)

__Scalar__- Quantity has magnitude only __Vector__- Quantity has magnitude **//__and__//** direction

**Motion Quantities:**
 * Time (scalar) t
 * Distance (scalar) x
 * Displacement (vector) **x -**x - change in position, length and direction between two points, symbol-∆x=Xf-Xi

**Speed vs. Velocity** Speed = Scalar (How fast an object is moving) Velocity = Vector (How fast __//**and**//__ in what direction an object is moving) Both are measured in Length over time (m/s, km/h)

**3** **Types of Motion so far:**  
 * At Rest
 * <span style="color: rgb(233, 12, 194);">Constant Velocity
 * <span style="color: rgb(209, 57, 234);"><span style="color: rgb(233, 12, 194);">Constant Acceleration
 * <span style="color: rgb(209, 57, 234);"><span style="color: rgb(233, 12, 194);">[[image:Picture_10.png]][[image:Picture_11.png]][[image:Picture_12.png]]

<span style="color: rgb(16, 229, 136);"><span style="color: rgb(16, 234, 108);"> Motion Diagrams:

Motion Diagrams, in addition to the graphs, are also an important part of this chapter. They demonstrate an object in motion. The spacing between the points shows what type of motion the object is under. Here are a few examples...

This is an object under constant velocity. You can tell because the spacing between the circles is equal.

This is showing an object that is accelerating positively, or speeding up. Notice how the spacing between the circles gradually increases.

<span style="color: rgb(30, 23, 196);">Motion Labs
<span style="color: rgb(30, 23, 196);"> The quicker you walk, the greater the slope. Away from origin is positive slope. Toward origin is negative slope. Straight line on DT graph = constant velocity. Curved line on DT graph = changing velocity and acceleration.
 * DT Graphs**:

Walking slower makes velocity slower. away, speeding up=positive acceleration Standing still makes a horizontal line at x-axis (0). towards,speeding up=neg.acceleration Walking away from origin, positive velocity. away,slowing down=neg.acceleration Walking toward the origin, negative velocity. towards,slowing down= pos.acceleration
 * VT Graphs:**

Positive acceleration is above x-axis. Negative acceleration is below x-axis. No acceleration is on the x-axis.
 * AT Graphs:**


 * DT Graph, slope = velocity
 * VT Graph, slope = acceleration
 * VT Graph, area under curve = distance
 * AT Graph, area under curve = velocity


 * Acceleration is a change in Velocity.
 * Velocity and Acceleration in same direction: speed increases.
 * Velocity and Accelerations in opposite directions: speed decreases.

__**Example:**__ <span style="color: rgb(30, 23, 196);"> Note: Speed **//__can't__//** change without velocity changing. Velocity **//__can__//** change without speed changing; direction can change Constant velocity = no acceleration Instantaneous velocity-speed at any given time A motion diagram is a picture of what is happening. - It compares distances at equal intervals of time.
 * <span style="color: rgb(30, 23, 196);">The object is moving away because the graph is above the x-axis* The object is accelerating from (0,2) and slowing down from (5,8)* The object has constant velocity from (2,5)* The acceleration can be found by taking the slope from (0,2) or (5,8).
 * To find instantaneous velocity, use slope of tangent line (at 1 point).

<span style="color: rgb(16, 198, 20);">**Motion Equations:** Practice Problems:
 * <span style="color: rgb(16, 198, 20);">[|Equations 1]
 * <span style="color: rgb(16, 198, 20);">[|Equations 2]
 * <span style="color: rgb(16, 198, 20);">[|Equations 3]

<span style="color: rgb(242, 38, 38);">**Acceleration Due to Gravity:** Origin of 9.8 m/s^2 media type="custom" key="266581" All things fall at the same acceleration due to gravity. media type="file" key="Movie 15.mov" 9.8m/s^2 32ft/s^2
 * Acceleration due to gravity:**

Use the same motion equations but x will be replaced with y and a replaced with g.

A ball thrown up will never stop accelerating (Until another force acts on it, like you catching it) even at it's peak the acceleration is never zero

some helpful links: http://www.physics4kids.com/files/motion_intro.html <span style="color: rgb(105, 236, 216);"> Derivations of Motion Equations V=∆X/∆T a=∆V/∆T V = V0 + at avg. V = (V0+ V)/2 Δx = (V0+ V)/2 * (Δt) V² = Vo² + 2a(Δx) Δx = V0t + ½ (at²)

When using the accleration rate due to gravity, change the equations by substituting g in for a. V = Vo + g*t y = Vo*t + .5*g*t^2 V^2 = Vo^2 + 2*g*y DT VT AT
 * Constant Velocity Graphs:**

DT VT AT
 * Constant Acceleration Graphs**

For more info about Motion Here's a Really cool website: http://www.vias.org/physics/wrapnt_acceleration_and_free_fall49.html

<span style="color: rgb(203, 15, 235);">**Sample Problems!** 1. Spiderman runs 20 meters in 5.32 seconds what is his average speed?

2. Superman is flying through the air when he sees a comet falling from the sky. He increases his acceleration uniformly from 50 m/s W to 65 m/s W in 10 sec. to save earth. What is his acceleration?

3. A bowling ball and a speck drop from the same distance. Excluding air resistance which hits the ground first?

Answers