LESSON 1 OF 3 · FREE · ABOUT 4 MINUTES

Choose a physical model before calculating

Connect the stated conditions to a law, then check units and direction.

The idea

A useful calculation begins with a physical model. Constant acceleration permits the standard motion equations; negligible external impulse permits momentum conservation; a frictionless spring system permits mechanical-energy conservation. These conditions are not interchangeable. In a collision, momentum may be conserved while kinetic energy decreases. For circuits and lenses, identify the arrangement before substituting numbers.

A method to try

  1. List the known values, the requested quantity and the conditions that remove complications.
  2. Choose the relationship that follows from those conditions. Write it symbolically before entering numbers.
  3. Keep one consistent set of units and include a direction when answering a vector question.
  4. Check the result a second way: compare with a limiting case, an energy balance, a circuit branch sum or a ray picture.
WORKED EXAMPLE

Follow the reasoning.

A 1.5 kg object initially moves at 2.0 m/s. A constant net force of 3.0 N acts in the direction of motion for 3.0 s. Find the final velocity and displacement.

  1. The force is explicitly the net force, so a = Fnet/m = 3.0/1.5 = 2.0 m/s². It is constant and parallel to the initial velocity.
  2. The final velocity is v = u + at = 2 + 2 × 3 = 8 m/s in the original direction. The displacement is s = ut + ½at² = 2 × 3 + ½ × 2 × 9 = 15 m.
  3. Check with the average velocity: (2 + 8)/2 = 5 m/s, and 5 × 3 = 15 m. The two calculations agree. If the given force were only one of several forces, the acceleration calculation would need their vector sum.
CHECK YOUR UNDERSTANDING

Think it through first.

Two carts stick together while external horizontal impulse is negligible. Which is guaranteed to be conserved during the collision: total horizontal momentum or total kinetic energy?

Show the explanation

Total horizontal momentum.

The negligible external impulse gives momentum conservation. Sticking is a perfectly inelastic collision, so kinetic energy is generally converted into other forms.

Make it your own

For each missed item, write the condition that justified the correct equation. Then change one number and solve again without looking at the answer.

This lesson is one part of a short starter pathway. It does not cover the full exam syllabus or establish a predicted score.

Official references

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