2.1 
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Interactive Simulations   Position and displacement in one dimension    Displacement and position in two dimensions    Solve v=dx/dt for dt    Velocity, position, and time (basic version)    Velocity, position, and time (more advanced version)    Acceleration (basic version)    Acceleration (more advanced version)    Static equilibrium    Static equilibrium and the lever    Newton's second law (basic version)    Newton's second law (more advanced version)    Circular motion interactive simulation    Orbits of the planets and dwarf planets    Orbits simulation Interactive Calculators   Speed calculator    Velocity calculator    Acceleration calculator    Velocity in accelerated motion    Average velocity calculator    Hooke's law calculator    Torque calculator    Rotational equilibrium and torque    Newton's second law calculator    Momentum calculator    Angular velocity    Linear velocity and angular velocity    Centripetal acceleration    Centripetal force    Law of universal gravitation calculator
1 - Science of Physics
2 - Forces and Motion      Chapter 2 at a glance      2.1 - Motion      2.2 - Force, momentum, and Newton's laws      2.3 - Circular motion      2.4 - Solving harder physics problems      2.5 - Chapter review3 - Energy Transformations4 - Waves and Sound
5 - Electricity and Magnetism
6 - Light and Optics
7 - The Atom
8 - Linear Motion
9 - Vectors and Forces
10 - Forces
11 - Newton's Laws and Gravitation
12 - Circular Motion and Gravitation
13 - Torque and Static Equilibrium
14 - Momentum and Collisions
15 - Angular momentum
16 - Power and Machines
17 - Harmonic Motion
18 - Waves
19 - Sound
20 - Electricity
21 - Electric and Magnetic Fields
22 - Electromagnetism and Induction
23 - Light and Color
24 - Geometrical Optics
25 - Electromagnetic Radiation
26 - The Properties of Matter
27 - Thermodynamics and Heat Transfer
28 - The Atom
29 - The Quantum Theory
30 - TBD
31 - TBD
32 - TBD
33 - TBD
34 - TBD
35 - TBD
36 - TBD
37 - The atomic nucleus and radioactivity
38 - Nuclear reactions
39 - Relativity
40 - Particle physics and the standard model
41 - Electronics (semiconductors)
42 - Nuclear technology
43 - Lasers and photonics
44 - Metals, alloys and materials science
45 - Communications technology
46 - Buildings and structures
47 - Energy technology
48 - Biophysics
49 - Matter and Energy, Space and Time
50 - Energy Transformations
51 - Nanotechnology
52 - Website Videos
53 - ExtraStuff
55 - Modeling Motion, Friction, and Center of Mass
56 - Work and the Conservation of Energy
Velocity, position, and time relationships
How do I use the velocity equation? Consider an object that starts at initial position, xi, and moves with constant speed, v. The equation for velocity can be rearranged into a model that relates final position xf to initial position xi, velocity v, and time t. Thinking about the equation as a model is useful because the model can be rearranged in different ways using algebra. Each is useful for solving a different variation of problems involving speed, distance, and time.
Solve v=dx/dt for dt
Three different ways to express the relationship between speed, position, and time
What does the sign of velocity mean? Velocity can be positive or negative depending on how you define direction. If moving to the right is defined to be positive then a negative velocity, such as −4 m/s, describes moving to the left. You should realize that this is a choice and not a rule of physics. You can choose any direction to be positive, including to the left instead of right, or up, or down. However, you must be consistent with your choice and not change it in the middle of solving a problem!
Positive and negative velocity
What does “constant speed” mean? Many problems include the term constant speed or constant velocity. This means the value of the velocity v does not change over time. For example, if a problem gives a “constant speed of 10 m/s,” then the velocity stays 10 m/s for all time of interest in the problem. Of course, no real speed stays constant for very long; in many circumstances, however, it is a good approximation. Show Velocity vs. speed
Initial time In many physics problems, it is convenient to set the initial time ti to zero. In such cases, the time interval becomes Δt = t and the initial position (at time zero) is written x = x0. Some books and resources use this alternate notation.
Test your knowledge Ryan moves to the right with a positive velocity of 5 m/s for 1 second, then to the left with a negative velocity of −5 m/s for 1 second. What is Ryan's displacement after the 2 seconds?
  1. 5 m
  2. 10 m
  3. 0 m
  4. -5 m
Show
Solved Problem 2.1: Time to get from A to B
A train starts in Chicago, passes through St. Louis after traveling 500 km and reaches Baltimore after traveling 1,900 km (total). If the train travels at a constant velocity of 75 kilometers per hour, then how long does it take to get from St. Louis to Baltimore?

Asked: Time from St. Louis to Baltimore
Given: xi = 500 km; xf = 1,900 km; v = 75 km/h
Relationships: t f = t i + x f − x i v
Solution: Let the time be ti = 0 when the train passes St. Louis. t f =0+ 1,900 km−500 km 75 km/hr =18.7 hr
Answer: 18.7 hours

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