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Physics · Grades 9–12

Momentum in one-dimensional collisions

Use signed velocities and a clearly chosen isolated system.

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Learn the idea

Momentum

Momentum is mass times velocity, so direction matters. Two opposite momenta may sum to zero.

Conservation

Total momentum is conserved when the external impulse on the chosen system is zero.

Sticking objects

If two objects stick together, their final velocity is common but kinetic energy generally decreases.

Energy distinction

A conserved momentum does not imply kinetic energy is conserved in every collision.

Worked examples

A 3 kg cart moves at −4 m/s. Find signed momentum.

p = mv = 3 × (−4) = −12 kg·m/s.

-12 kg·m/s

A 2 kg cart at 6 m/s sticks to a 4 kg stationary cart. External impulse is zero. Find final velocity.

Initial momentum is 12; divide by combined mass 6 kg.

2 m/s

Check your understanding

  1. When is total momentum conserved for a chosen system?

    1. Only when objects have equal masses
    2. Whenever one object stops
    3. When net external impulse is zero

  2. Two momenta are +15 and −9 kg·m/s. Find their total.

  3. Why must westward and eastward velocities not both be inserted as positive in a one-axis collision model?

Answers and marking notes

Answers and marking notes
  1. When net external impulse is zero

    External impulse determines the change in total system momentum.

  2. 6 kg·m/s

    Signed addition gives 15 − 9 = 6 kg·m/s.

  3. They point in opposite directions and therefore need opposite signs on the same axis.

    Credit a consistent direction convention.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Independent educational review required. Grade bands are approximate; these are not officially aligned curricula.