Constant Motion Equations
Demonstration of the relationship between the three terms in the equation of motion: x(t) = 1/2 at2 + vot + xo and the three types of associated constant motion: constant acceleration, constant velocity, and constant position. Constant Motion Equations QT Movie.
Constant Acceleration Variable Association
Displayed is the motion of two cars undergoing constant acceleration. The objective is to adjust the initial position, initial velocity, and initial acceleration of a blue car so that it matches the motion of the yellow car. There are several possible causes of the yellow car's motion, all of which are unknown.
Comparison of Accelerations
The acceleration and initial velocities of four objects can be adjusted, in order to visually compare them undergoing different constant accelerations.
Constant Velocity Space-Time Diagram
The Space-Time diagram for four objects undergoing constant velocity in a straight line can be observed. The Constant Velocity Space-Time Diagram QT Movie
Space-Time Diagram
The Space-Time diagram is generated for four object undergoing three different types of constant motion in a straight line: constant acceleration, constant velocity, and constant position.
Velocity-Time and Space-Time Diagram for Constant Acceleration
Both the Velocity-Time and the Space-Time diagram are generated for a single body undergoing uniform acceleration. Both the initial position and initial velocity can be varied as well as the body's acceleration.
Velocity-Time Diagram for Two Bobs undergoing Complex Motion
A double pendulum is constructed using two bobs connected by rigid rods. The velocity versus time diagram is displayed for the magnitude of each bob's velocity. Velocity-Time Diagram for Two Bobs QT Movie
Gravitational Free-Fall
An object can be given an initial vertical velocity (either positive or negative) and an initial height above the ground. Displayed is the motion of the object, along with both the distance vs. time and velocity vs. time diagrams.
Law of Falling Bodies:
Two identical objects differing only in mass are dropped from the same height at the same time. With air resistance set to zero, both objects strike the ground at the same time. As the air resistance is increased, the more massive object will strike the ground first. With enough air resistance, the lighter object is seen to reach a constant terminal velocity. Displayed is the distance vs. time, velocity vs. time, and the acceleration vs. time diagrams.
Car Braking to a Halt Simulation
A moving car brakes to a halt in a fixed amount of time. Observed is the distance the car travels while braking to a stop. The car's initial speed and braking time can be varied. Braking Car Problem and Braking Car QTMovie (236K)
Smoking Driver Simulation
A driver looks away to dial a cellular phone or to light a cigarette. Observed is the distance the car travels during the distraction. The car's speed and the duration of the distraction can be adjusted. Distracted Driver Problem - Distracted Driver QT Movie (160K)
Vertical Ball Toss Simulation
A ball is launched vertically into the air along side a tall building. The objective is to make the maximum rise of the ball equal the height of the building by adjusting the ball's initial upward velocity, . Vertical Ball Toss Problem - Vertical Ball Toss QT Movie (500K)
Police Car Chase Simulation
A speeding station wagon passes a parked police car. The police car begins to accelerate at the moment that the station wagon passes. The station wagon's speed and the police car's acceleration can be varied to determine the moment when the police car is moving at the same speed as the station wagon, the moment when it catches the station wagon, and the distance it takes to overtake the wagon. Police Chasing Station Wagon Problem - Police Car Chase QT Movie (500K)
Ladybug on a Skateboard Calculus-of-Motion Simulation
The equations of motion for a ladybug's velocity is given to be v(t) = a(t- t)2- b. Displayed is her one-dimensional motion along, with the x vs. t, v vs. t, and a vs. t diagrams. Also noted are the moments when the ladybug reverses directions, changes velocity, and acceleration. Calculus-of-Motion Problem - Ladybug QT Movie(500K)
Rising Rocket Problem
A toy rocket has an upward acceleration until its fuel runs out. The speed and height of the rocket are observed in order to determine the maximum height, velocity, and duration of the flight. Both the acceleration and burnout time can be adjusted. Rising Rocket Problem - Rising Rocket QT Movie (375K)