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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
Position versus time graph
A driving trip Consider a trip between Wilmington, Delaware and Washington, DC, which are 160 kilometers (98 miles) apart. You drive at 100 km/h (62 mph) for 1 hour, take a 24 minute rest, then drive for another 36 minutes at the same speed. You travel 160 kilometers in two hours so your average speed is 160 km ÷ 2 hr = 80 km/h. According to your speedometer, however, this is not the speed you actually drove! Did you drive at a speed of 100 km/h or 80 km/h?
What does the position vs. time graph show? Graphical plot of position versus time for a trip from Wilmington to Washington, D.C. The position versus time (or x vs. t) graph is an accurate record of actual speeds. The origin is Wilmington, DE. The graph shows position along the road x on the vertical axis and time t on the horizontal axis. In the first hour your position changed from zero to 100 kilometers. For the next 24 minutes the graph is flat. This shows a constant position—you were stopped. The final 36 minutes shows a position change of an additional 60 kilometers.
How is speed related to slope? The slope of a line is the ratio of rise over run, or change in the vertical axis divided by change in the horizontal axis. The speed on a distance vs. time graph is the slope of the line. On the x vs. t graph staying at rest creates a flat line, or a slope of zero. In the example, over the first hour the change in position is 100 km and the change in time is 1 hour, giving a speed (slope) of 100 km/h.
Concept of slope in math and physics graphs
Show Slope in math and physics
How does the graph show moving backwards? Suppose you turn around in Washington and head right back. The position versus time graph shows the return trip as the downward sloping line (below) starting at t = 120 minutes. A negative slope means travel towards the origin. A positive slope for the first part of the trip meant travel away from the origin. In both cases the velocity is the slope of the position vs. time graph—only that the velocity is negative for the return trip.
Position versus time plot for outgoing and return trip
Test your knowledge Jake travels at a constant speed of 50 km/h towards his destination 250 km away. How long does it take him to arrive?
  1. 5 hours
  2. 4 hours
  3. 3 hours
  4. 2 hours
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