2.4 
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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
Using information and combining equations
What is contextual information? Solving most problems and real-life situations involves creatively using the information you know, and also deducing information that is not stated but implied by the context of the problem. Unless otherwise stated you should assume the following in many problems. If you are stumped, think about what assumptions you might make that would make a problem solvable.
  1. Treat the problem as if friction were zero unless given a friction force.
  2. Assume given velocities are constant unless forces or accelerations are known.
  3. Choose initial position, initial time, and initial velocity to be zero unless you know otherwise.
  4. Try to relate all the information you are given to the variables you chose.
How do I use the distance? The problem says the two bicycles are 500 meters apart at the start, which is t =  0. To use this information we need to relate it to the distance variables we defined. At the time when they meet, the total distance traveled by both bicycles together has to be 500 meters. In our variables, that means d1 + d2 = 500 m. This provides a needed third equation for the problem. However, there is still one more needed. We need four equations or relationships to find four unknown values.
Constructing an equation from the wording of the question
Deducing implied information The last equation comes from reading the problem and recognizing that the bicyclists meet after traveling the same amount of time after starting 500 meters apart. Mathematically, that means t1 = t2 = t. Since the times are equal, they do not need subscripts to tell them apart. We can write the three equations in terms of a single time, t.
Solving multiple equations with multiple unknowns
How do I use multiple equations? We now have enough to solve the problem. The unknown distance d1 = v1t. The unknown distance d2 = v2t. This is true no matter what value t has. The distance relationship tells you that d1 + d2= 500 m therefore replace the distances with their equivalent velocities and times. This gives you a single equation with a single unknown value. THAT is what you want because then you can calculate an answer.
Solution for the problem

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