Worked example
A 2 kg cart at +6 m/s sticks to a stationary 4 kg cart. External impulse is negligible. What is their shared final velocity?
Answer & why
Answer: 2 m/s
Initial momentum = 2 × 6 = 12 kg·m/s; combined mass = 6 kg; v = 12 ÷ 6 = +2 m/s.
Grade 12 · Science
Conserve momentum in a one-dimensional model
Use signed momentum and a stated negligible external impulse to calculate a joined system’s final velocity.
6 authored questions + worked example
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All questions
All 6 authored questions for this skill.
Question 1
Two 2 kg carts approach at +3 m/s and −3 m/s and stick. External impulse is negligible. What is their shared final velocity?
- 0 m/s
- 2 m/s
- 1 m/s
- 3 m/s
A hint
Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
Answer & why
Answer: 0 m/s
Their momenta cancel: 6 + (−6) = 0; the joined carts have zero final velocity.
Question 2
A 1 kg cart at +4 m/s sticks to a stationary 3 kg cart with negligible external impulse. What is the final velocity?
- 4 m/s
- 1 m/s
- 2 m/s
- 3 m/s
A hint
Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
Answer & why
Answer: 1 m/s
Total momentum = 4 kg·m/s and total mass = 4 kg, giving +1 m/s.
Question 3
A 2 kg cart at +8 m/s sticks to a stationary 2 kg cart with negligible external impulse. What is the final velocity?
- 2 m/s
- 4 m/s
- 3 m/s
- 1 m/s
A hint
Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
Answer & why
Answer: 4 m/s
Total momentum = 16 kg·m/s; dividing by 4 kg gives +4 m/s.
Question 4
A 1 kg cart at −4 m/s sticks to a stationary 3 kg cart with negligible external impulse. What is the final velocity?
- 3 m/s
- 1 m/s
- 2 m/s
- −1 m/s
A hint
Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
Answer & why
Answer: −1 m/s
Momentum is −4 kg·m/s; divided by 4 kg, the shared velocity is −1 m/s.
Question 5
A 2 kg cart at +6 m/s sticks to a stationary 4 kg cart. External impulse is negligible. What is their shared final velocity?
- 1 m/s
- 4 m/s
- 3 m/s
- 2 m/s
A hint
Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
Answer & why
Answer: 2 m/s
Initial momentum = 2 × 6 = 12 kg·m/s; combined mass = 6 kg; v = 12 ÷ 6 = +2 m/s.
Question 6
A 3 kg cart at +4 m/s sticks to a stationary 1 kg cart with negligible external impulse. What is the final velocity?
- 1 m/s
- 3 m/s
- 2 m/s
- 4 m/s
A hint
Choose a positive direction and calculate total initial momentum as the sum of mass × signed velocity.
Answer & why
Answer: 3 m/s
Total momentum = 12 kg·m/s and total mass = 4 kg, giving +3 m/s.