LESSON 2-4: Acceleration

Transcription

1 DEVIL PHYSICS BADDEST CLASS ON CAMPUS PRE-IB PHYSICS LESSON 2-4: Acceleration 1. Objectives. By the end of this class you should be able to: a) SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference ) as functions of time. (High) b) Understand that average acceleration is defined as the change in velocity divided by the time required to make this change. c) Understand that instantaneous acceleration is defined as the change in velocity divided over an infinitesimally short period time. d) Calculate acceleration when given change in velocity and change in time

2 e) Calculate change in time when given change in velocity and acceleration f) Calculate change in velocity when given change in time and acceleration g) Calculate starting or ending velocity when given one of the two, acceleration and change in time 2. Average acceleration a) the change in velocity divided by the time required to make this change b) the bar over the a indicates average c) means change in d) acceleration can be either positive or negative i) negative acceleration is often called deceleration 3. Units a) typical units for acceleration are m/s 2 b) but can be any unit of length over, or per, unit of time squared 4. Instantaneous acceleration

3 a) the change in velocity over an infinitesimally short period of time SAMPLE PROBLEMS 1. I am driving at 15 m/s behind a big truck. I punch the accelerator to pass the truck and 18 seconds later I am at 25 m/s. What was my average acceleration? 2. While travelling at 30m/s, I decide to stop using an average acceleration (deceleration) of -2.13m/s 2. How long will it take me to stop?

4 Units: LESSON 2-5: Motion at Constant Acceleration 1. Objectives. By the end of this class you should be able to: a) SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference ) as functions of time. (High) 2. Uniformly accelerated motion occurs when acceleration is constant and in a straight line a) Assume that we are starting at a time of zero, so

5 t 1 = 0, so we ll call it t 0 instead and call the final time (t 2 ) just t to be consistent, we ll call the initial position (x 1 ) x 0 instead and call the final position (x 2 ) just x b) Therefore, the equation for average velocity becomes (since t 0 = 0) c) The equation for constant acceleration becomes (no bar over a because it is now constant instead of an average) d) A common problem is to find the velocity after an object has accelerated for a given period of time. To do this, we solve the constant acceleration equation for velocity:

6 e) Next, we will find position after traveling at a certain average velocity for a given period of time: f) Now we will find the position of an object after undergoing constant acceleration for a given time, t: Average velocity is the velocity midway between initial and final velocities: This can be substituted into our equation for displacement:

7 We can then substitute our equation for v ( ) into the above equation: If we multiply it out: g) We now derive a fourth equation that is useful when elapsed time is not known. We start at a point near the beginning of the last derivation: Next, we solve the equation for t:

8 We not substitute this value of t into the displacement equation above: Using FOIL (or difference of two squares) we can multiply this out to: We now solve for v 2 :

9 Rearranging we get: h) Anybody need an aspirin? 3. Summary of 1 dimensional motion at constant acceleration: a) The following four equations apply when a is constant: LESSON 2-6: Solving Problems Everyone read the Problem Solving section on Giancoli page29 1. Read the problem. 2. Draw a picture with set of coordinate axes at reference point.

10 3. Write down the knowns or givens and what you are trying to find. Convert givens to compatible units. 4. Select appropriate equations. Ensure they are valid for the situation. 5. Carry out calculations. 6. Estimate calculations to ensure answer is reasonable. 7. Ensure your units cancel out. Period X STOPPED HERE SUMMARY 1. Objectives. Are you able to: a) SC.912.P.12.2: Analyze the motion of an object in terms of its position, velocity, and acceleration (with respect to a frame of reference ) as functions of time. (High) b) Understand that average acceleration is defined as the change in velocity divided by the time required to make this change.

11 c) Understand that instantaneous acceleration is defined as the change in velocity divided over an infinitesimally short period time. d) Calculate acceleration when given change in velocity and change in time e) Calculate change in time when given change in velocity and acceleration f) Calculate change in velocity when given change in time and acceleration g) Calculate starting or ending velocity when given one of the two, acceleration and change in time