LESSON 2-2: Motion With Constant Acceleration

Transcription

1 DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS 2 LESSON 2-2: Motion With Constant Acceleration 1. Objectives. By the end of this class you should be able to: a) Recognize situations of accelerated motion and to define acceleration as. b) Describe a motion given a graph for that motion. c) Understand that the slope of a displacementtime graph is the velocity. d) Understand that the slope of a velocity-time graph is the acceleration and the area under a velocity-time graph is the change in displacement

2 e) Analyze motion from ticker tape, stroboscopic pictures, and photogate data f) Solve problems of kinematics for motion in a straight line with constant acceleration using: 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

3 b) but can be any unit of length over, or per, unit of time squared 4. Instantaneous acceleration 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: 5. 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 b) Therefore, the equation for average velocity becomes (since t 0 = 0) c) The equation for constant acceleration becomes

5 (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: e) Next, we will find position after traveling at a certain average velocity for a given period of time:

6 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: We can then substitute our equation for v ( ) into the above equation:

7 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: We not substitute this value of t into the displacement equation above:

8 Using FOIL (or difference of two squares) we can multiply this out to: We now solve for v 2 : Rearranging we get: h) Anybody need an aspirin? 6. Summary of 1 dimensional motion at constant acceleration: a) The following four equations apply when a is constant:

9 7. Acceleration Due To Gravity a) Since the earth is rotating, why don t we all fly off into space like a kid falling off a merry-goround? b) Law of gravitational attraction: c) What order of magnitude is the force? d) Is acceleration due to gravity 9.81 m/s 2 everywhere on earth? e) Signs of the times. 8. Graphical Analysis of Motion

10 Circumference C/mm y = x R² = Diameter d/mm a) Displacement vs Time Graphs

11 Period 5 STOPPED HERE

12 b) Velocity-Time Graph

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15 c) Acceleration-Time Graphs Measuring Speed and Acceleration See Text

16 SUMMARY 5. Objectives. By the end of this class you should be able to: a) Recognize situations of accelerated motion and to define acceleration as. b) Describe a motion given a graph for that motion. c) Understand that the slope of a displacementtime graph is the velocity. d) Understand that the slope of a velocity-time graph is the acceleration and the area under a velocity-time graph is the change in displacement e) Analyze motion from ticker tape, stroboscopic pictures, and photogate data f) Solve problems of kinematics for motion in a straight line with constant acceleration using:

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