Newton's Second Law as a Differential Equation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Force rules become motion equations

Science · Forces & Motion · ages 18-19
Name ______________________   Date ____________

  1. Inside forces between parts of the system cancel and do not affect its motion.

    Circle one:   True   False

  2. What is the first step before writing any equation of motion?

    • List the outside forces
    • Guess the final position function
    • Solve for the starting velocity

  3. Why is F equals m a a differential equation for position?

    • Because mass always changes with time
    • Because force is always constant
    • It is the second slope of position

  4. The pull on a mass fades as time passes. How do you find its motion?

    • Use the steady force parabola anyway
    • Integrate the changing force over time
    • Read the answer straight off the force rule

  5. A mass is pulled by a steady force. What shape does its position graph have?

    • A straight line
    • Parabola in t squared
    • A flat horizontal line

  6. You solved the equation of motion but gave no starting values. What do you have?

    • Many possible trips
    • The one true trip of the mass
    • A proof that the force must be zero

  7. A 2 kg mass feels a steady net force of 6 newtons. What is its acceleration in meters per second squared?

    Answer: ______________

  8. A student writes F equals m a for a fading pull and claims the motion is solved. What is the error?

    • The law itself hands over the position function
    • Only the equation, which needs solving
    • The law does not apply when force changes
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Force rules become motion equations W1-mt_LzSNSkEovH-s1

  1. True · Only outside forces change the motion of the chosen system.
  2. List the outside forces · You must inventory each push and pull, with direction, before any equation makes sense.
  3. It is the second slope of position · Replacing acceleration with x double prime turns the law into mass times x double prime equals force.
  4. Integrate the changing force over time · A force that varies with time demands integration, since the parabola only fits constants.
  5. Parabola in t squared · Integrating a constant twice puts t squared into the position function.
  6. Many possible trips · One equation with a second slope admits many paths until starting values select one.
  7. 3 · Acceleration is net force over mass, so 6 divided by 2 gives 3.
  8. Only the equation, which needs solving · Writing the equation states the problem. Solving it with both starting values gives the motion.
Worksheet · LightMySky