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
Speed and velocity
3-D and 1-D A GPS receiver describes the location of a car with its longitude (east-west), latitude (north-south), and height above sea level. This is a three-dimensional description because it requires three numbers. However, if all we want to know is where the car is along the road we can stretch the road out into a straight line and provide the one-dimensional position with a single value—such as mile post 167. When position can be described by a single value we say the description is one-dimensional.
What is speed? A one-dimensional definition of speed is the ratio of the distance traveled divided by the time taken. This is equation (2.1) and you have probably seen it before. If you go 120 miles in 2 hours your speed is the distance divided by the time, or 120 ÷ 2 = 60 miles per hour. In physics, we will usually use meters and seconds instead of miles and hours. Sixty miles is 96,558 meters, and 1 hour = 3,600 seconds, so 60 mph is the same speed as 26.8 meters per second (m/s). Show Speeds in physics
Speed calculator
(2.1) v= d t
v  = speed (m/s)
d  = distance traveled (m)
t  = time taken (s)
Speed
elementary definition
What is velocity? Equation (2.1) is limited because a distance can be zero or positive but not negative therefore speed is always positive. To account for moving backward we extend the concept of speed to include velocity, v. The velocity is defined by equation (2.2).
Velocity calculator
(2.2) v= Δx Δt
v  = velocity (m/s)
Δ x  = change in position (m)
Δ t  = change in time (s)
Velocity
improved definition
How are speed and velocity different? The symbol “Δ” translates to “the change in” and is pronounced “Delta.” Since x is position, Δx therefore means “the change in position.” Equation (2.2) is a better definition because velocity is the change in position divided by the change in time. Because positions can be in front, or behind, the velocity can be positive or negative. Velocity has the same units as speed and has the same meaning in terms of describing how fast an object is moving. Velocity has the additional capability, however, of being positive or negative, thereby indicating the direction of motion as well as the speed. Mathematically, the speed (2.1) is the absolute value of the velocity (2.2). Show More on the difference between speed and velocity
Initial and final A change in a quantity is often described using the initial and final values. The displacement in position in equation (2.2) is Δx = xf − xi. Likewise, the time interval in equation (2.2) is Δt = tf − ti. Why do these expressions subtract final minus initial, not initial minus final? Consider the case where you ran a 100 m sprint from the start line at xi = 0 m to the finish line at xf = 100 m. Your displacement is Δx = xf − xi = +100 m, not xi − xf = −100 m. You ran forwards (+100 m) not backwards (−100 m)!
Test your knowledge 1) An arrow travels 25 meters in 0.1 seconds. The speed of the arrow is closest to:
  1. 0.004 m/s
  2. 2.5 m/s
  3. 25 m/s
  4. 250 m/s
Show
2) Which is a correct statement about speed and velocity?
  1. Speed is faster than velocity.
  2. We encounter speed but not velocity in everyday uses.
  3. Velocity has direction while speed does not.
  4. Speed can be negative while velocity cannot.
Show

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