Chapter 3

3.1 Acceleration  How do you know when velocity is changing? What do you experience?  Particle-models can represent velocity Evenly spaced dots = constant velocity Dots spreading further apart = speeding up Dots moving closer together = slowing down Changing Velocity

Motion Diagrams  On a motion diagram, velocity is represented using average acceleration vectors.  To find average acceleration, subtract two consecutive velocity vectors. Then divide by time interval. The difference between two velocity vectors represents ΔV

Positive and Negative Acceleration Positive AccelerationNegative Acceleration  Velocity vectors and acceleration vectors point in the same direction  Object speeds up in the positive direction  Slowing down in the negative direction  Velocity vectors and acceleration vectors point in opposite direction  Object slows down in the positive direction  Object speeds up in the negative direction This will all be easier to see on an Velocity – Time Graph! Be Careful! Sign of acceleration DOES NOT indicate speeding up or slowing down!

Velocity – Time Graphs What can we determine about the motion of an object by looking at a Velocity – Time graph?

Velocity – Time Graphs  Slope of line represents acceleration.  Average acceleration is defined as the change in velocity during some measurable time interval divided by that time interval.  Instantaneous acceleration is the change in velocity at an instant of time. Found by drawing a line tangent to the time you are interested in on a velocity-time graph. We generally will not solve for instantaneous acceleration in this class. (Calculus!)

Velocity – Time Graphs  Remember: Slope indicates acceleration  Area Under the Curve Indicates Displacement!  Using slope formula, and equation for acceleration can be derived. SI Unit for acceleration is m/s 2

Velocity – Time Graphs Describe the motion of each object as represented on the velocity – time graph! Velocity (m/s) Time (s)

3.2 Motion with Constant Acceleration  Using the equations for average velocity and average acceleration, we can come up with (derive) several equations for motion with uniform acceleration.  Depending on variables known or given, these equations can be used to solve for v f, v i, d f, d i, a, or t.

Velocity with Average Acceleration  The final velocity is equal to the initial velocity plus the product of the average acceleration and time interval.  This equation is simply the average acceleration equation rearranged.

Position with Constant Acceleration  An object’s position at a time after the initial time is equal to the sum of its initial position, the product of the initial velocity and the time, and half the product of the acceleration and the square of the time.  This equation is derived from a velocity vs. time graph.velocity vs. time

An Alternative Expression  Sometimes a time interval is not known and we will still need to relate position, velocity, and acceleration.  Rearranging and substituting the last two equations will give us the equation

Summary of Equations Making a “Given” and “Find” column when you do problems will help you decide which equation to use for each problem. PRACTICE is the best way to figure this out.

3.3 Free Fall  Galileo Galilei is credited with doing the first real studies on the effects of gravity.  His conclusion: neglecting the effect of the air, all objects in free fall has the same acceleration.  Substance, mass, or height of drop have no significant effect on acceleration due to gravity.  g = 9.8m/s 2

Acceleration Due to Gravity  Acceleration of an object in free fall that results from the influence of Earth’s gravity.  For each second in free fall, velocity will increase by 9.8m/s.  In each second, the distance will become successively larger.

Positive or Negative  When analyzing free fall, treating acceleration as positive or negative depends on the coordinate system used.  If up = positive, then acceleration is –g  If down = positive, then acceleration is +g

Ball Thrown Upward  If you thrown something upward and choose up as positive then Object leaves hand with positive velocity Acceleration is downward so use –g Velocity and acceleration are in the opposite direction, speed of ball decreases  What is the value for g at the top of the throw? Explain.

Graphing Free Fall  What would a Velocity-Time Graph look like for an object in free fall? (Up is positive.)  What would a Position-Time Graph of the same motion look like?