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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
Acceleration on motion graphs
Acceleration as the slope of a speed versus time graph
Acceleration is slope on a v vs. t
graph		 Acceleration causes a non-zero slope on the velocity versus time graph, because acceleration represents change in velocity over time. Mathematically, the slope of a v vs. t graph is the change in velocity divided by the change in time, which is the definition of acceleration. In the example above, velocity increases at a steady rate of 0.5 m/s each second, producing a straight-line with a slope of 0.5 m/s2. Show Positive velocity with negative acceleration
Why is the
x vs. t
graph a curve?		 Accelerated motion looks different on the v vs. t and x vs. t graphs. Constant acceleration means the velocity changes the same amount every second—producing a straight line on a v vs. t graph. But now let's consider how this motion looks on a x vs. t graph. A moving object with an increasing velocity covers more distance during each new second than it covered in the previous second. That means the slope of the x vs. t graph must become steeper over time as the velocity increases. The changing slope is what we recognize as a curve. In general, acceleration results in curves on the x vs. t graph.
Velocity vs. time and position vs. time graphs
Constant acceleration versus constant velocity Constant velocity, or constant speed, both mean that the acceleration is zero. The position changes by the same amount in equal time intervals and the result is a flat v vs. t graph and a constant-slope x vs. t graph. Constant acceleration means the velocity changes by an equal amount in equal time intervals. This means a constant-slope v vs. t and a curved x vs. t graph.
Position and velocity graphs for constant velocity and constant acceleration
Test your knowledge Constant positive acceleration looks like which of the following on a velocity vs time graph?
  1. Linear positive slope
  2. Curved positive slope
  3. Linear negative slope
  4. Curved negative slope
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