# Kinematics in One Dimension

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations
Videos

Student Learning Objectives

• To differentiate between the concepts of position, velocity, and acceleration.
• To recognize the relationship between velocity and acceleration when an object is speeding up, slowing down, or turning.
• To interpret kinematic graphs and to relate position, velocity, and acceleration graphs to each other.
• To begin the development of a robust problem-solving strategy.
• To solve quantitative kinematics problems, including objects falling under the influence of gravity.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY105 Notes from Boston University (algebra-based):

Introductory physics notes from University of Winnipeg (algebra-based):

HyperPhysics (calculus-based)

PHY2048 notes from Florida Atlantic University (calculus-based):

PHY2043 notes from Florida Atlantic University (calculus-based)

General Physics I notes from ETSU (calculus-based)

Important Equations

Example Problems

Problem 1
Starting from rest, a car accelerates at a constant 4.00 m/s2 for a distance of 425 m. The car is then shifted into neutral and slows down at a rate of 2.25 m/s2. How much time elapses between when the car starts and when it stops? (Solutions)

Problem 2
A hot-air balloon is rising upward with a constant speed of 3.50 m/s. When the balloon is 115 m above the ground, a passenger trying to take a picture accidentally drops his cell phone over the side of the balloon. Ignoring air resistance, how much time elapses before the cell phone hits the ground? (Solutions)

Applets and Animations

 Displacement and Distance A simple animation showing the difference between the distance and the displacement. Motion Diagram A car with a non-zero initial speed has a constant acceleration whose value can be controlled by the user. Constant Acceleration 1-dimensional kinematics of a body undergoing constant acceleration. Includes visually integrating the acceleration and velocity graphs, and visually differentiating the position and velocity graphs. Motion with Constant Acceleration This Java applet shows a car moving with constant acceleration. The green control panel contains text fields where you can vary the values of initial position, initial velocity and acceleration. The applet shows the motion of the car as well as graphs of x, v, and a. One-Dimensional Kinematics This applet show position, velocity, and acceleration graphs for 6 different scenarios. It also includes an option where you can edit the velocity vs. time graph. The Moving Man Learn about position, velocity, and acceleration graphs. Move the little man back and forth with the mouse and plot his motion. Set the position, velocity, or acceleration and let the simulation move the man for you. Maze Game Learn about position, velocity, and acceleration in the "Arena of Pain". Use the green arrow to move the ball. Add more walls to the arena to make the game more difficult. Try to make a goal as fast as you can. Racing Balls Two balls roll down two different low-friction tracks near the Earth's surface. The user is invited to predict which ball will reach the end of the track first. Racing Skiers Same as the above animation except with skiers. Galilean Relativity Illustrating Galilean relativity using his example of dropping a ball from the top of the mast of a sailboat. Car on Inclined Plane The Car on an Inclined Plane model displays a car on an incline plane.  When the car reaches the bottom of the incline, it can be set to bounce (elastic collision) with the stop attached to the bottom of the incline.  The car consists of the car body, two rotating front wheels, and two rotating rear wheels. Rocket Car on Inclined Plane The Rocket Car on an Inclined Plane model displays a car on an inclined plane.  When the car reaches the bottom of the incline, it can be set to bounce (elastic collision) with the stop attached to the bottom of the incline.  The car consists of the car body, two rotating front wheels, and two rotating rear wheels. Ceiling Bounce The Ceiling Bounce Model shows a ball launched by a spring-gun in a building with a very high ceiling and a graph of the ball's position or velocity as a function of time.  Students are asked set the ball's inital velocity so that it barely touches the ceiling.

Videos

 Download video (5.3 Mb) Watch Streaming Great video showing a feather and a hammer dropped at the same time on the moon. Newton's Laws predict that they will both hit the ground at the same time in the absence of air resistance. (Notice how long it takes them to fall compared to the time it would take on earth.)