AP Physics B Summer Course 年 AP 物理 B 暑假班 M Sittig Ch 11: Kinematics

Describing motion Scalars  Distance  Speed  … Vectors  Displacement  Velocity  Acceleration  Jerk… Not commonly used.

Practice Problem  Mr. Ant, standing in an elevator, moves up 40 m with the elevator. He then gets out of the elevator and walks along a straight hallway for 3 minutes at a speed 10 meters/minute. What is the magnitude of Mr. Ant’s net displacement?

What is the difference between…  Speed  Average velocity  Velocity  Instantaneous velocity  Acceleration

Practice Problem  Which of the following cars has a westward acceleration?  A car traveling eastward and speeding up. A car traveling westward and slowing down. A car traveling westward at constant speed. A car traveling eastward and slowing down.

Solving kinematics problems  Remember the fundamental kinematics equations.  Know which quantities each equation has, and doesn’t have.  Fundamental kinematics equations only apply for constant velocity.  Use the table of variables – unique to 5S, and very useful!

Fundamental kinematics variables

Fundamental kinematics equations Number of stars = how many exponents each equation has.

Physics Problem Solving

Kinematics Problem Solving  Step 1: Write out all five variables in a table. Fill in known values, put “?” next to unknown values.  Step 2: If 3 or more known values, continue to Step 3. Otherwise, check your work.  Step 3: Choose the equation that has all of the knowns and the desired unknown. Solve.  Step 4: Put the correct units on your answer.

Example Problem

Practice Problem

Freefall  Acceleration due to gravity is a = -10 m/s 2 when gravity is the only force on the object.  The horizontal motion of an object will NOT affect its fall – time to fall depends only on the vertical position/motion.

Example Problem  What is the watermelon’s velocity when it hits the ground?

Practice Problem  What is the watermelon’s velocity when it hits the ground? downward

Projectile Motion  Break the velocity into vector components.  We can work with the vector components separately because they are independent of each other.  The y-component of velocity, v y, equals v(sin θ).  The x-component of velocity, v x, equals v(cos θ).  Horizontal velocity is constant.  Vertical acceleration is g, directed downward.  Time is the variable that is the same for x and y.

Example Problem

Practice Problem v

 5S pg 121 #4

Motion Graphs  The slope of a position–time graph at any point is the velocity of the object at that point in time.  The slope of a velocity–time graph at any point is the acceleration of the object at that point in time.  The area under a velocity–time graph between two times is the displacement of the object during that time interval.

Describe the motion

Practice Problem  The following data shows the positions of a car at times 0, 2, 4, 6, 8 and 10 s. Match the list of positions with the graph to which it corresponds.  0.0, 32.5, 65.0, 97.5, 130.0, m.  0.0, 8.0, 32.0, 72.0, 120.0, m.  0.0, 55.0, 120.0, 168.0, 168.0, m.

Practice Problem  The graph shows the speed of a car traveling in a straight line as a function of time.  The value of V c is 3.80 m/s and the value of V d is 5.30 m/s. Calculate the distance traveled by the car from a time of 1.20 to 5.20 seconds.

Super Challenge Problem  A student walks into an elevator at rest on the bottom floor of a building with 4 stories. The elevator then accelerates upward with an unknown constant acceleration a during a time interval Δt1 = t, moves at a constant velocity for Δt2 = 6t, and then decelerates at the same magnitude a for time interval Δt3 = t. If the elevator rises a total of h meters, what is the magnitude of the acceleration a given time t and height h?