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 versus time graph
Velocity vs. time graph for the car trip The velocity versus time (or v vs. t) graph shows velocity on the vertical axis and time on the horizontal axis. This provides a quick visual history of how the velocity changes. The v vs. t graph can fool you, however, unless you remember that the y-axis is velocity, not position!Position and speed versus time graphs for a trip between Wilmington and Washington, D.C.
Interpreting the v vs. t graph The diagram on the right shows the x vs. t and v vs. t graphs for trip from Wilmington to Washington. Note the differences in how constant velocity appears on both graphs. The motion is the same in both the graphs, but the way the motion appears on the two graphs is quite different:
  1. Constant speed is a sloped line on the x vs. t graph but a flat line on the v vs. t graph.
  2. The slope of the x vs. t graph is equal to the value of the v vs. t graph at the same time interval. In the example, during the first hour the slope is 100 km/h and this is the value of the v vs. t graph for the first hour.
  3. Zero velocity lies on the x-axis where the y-axis has a value of 0 km/h.
Distance from a v vs. t graph To find the distance traveled from a velocity versus time graph we use a graphical interpretation of the equation d = vt. Consider the orange shaded rectangle on the v vs. t graph below. This rectangle fills the area between the line representing velocity and the x-axis where v = 0. Now consider that the area of a rectangle is equal to its length times its height. On the v vs. t graph, length is equal to time and height is equal to velocity. Therefore, area on the graph is velocity multiplied by time, which is the distance traveled. This is an important result! Area on a v vs. t graph represents distance.
Distance traveled is the area on a speed versus time graph
Connecting the two graphs We have now learned that there are two important ways that position vs. time and velocity vs. time graphs are related to each other:
  1. The slope of a distance vs. time graph is velocity; and
  2. The area under a velocity vs. time graph is the total distance traveled.
Test your knowledge A line segment with a linear negative slope on a position vs time graph represents what on a velocity vs time graph?
  1. A positive slope
  2. A slope of zero below the origin (horizontal line stemming from below zero)
  3. A negative slope
  4. A slope of zero above the origin (horizontal line stemming from above zero)
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