Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Use final minus initial signed velocity, not a difference of speed magnitudes.
Worked solution
(a)
Use final minus initial signed velocity, not a difference of speed magnitudes.
Subtract the pre-collision velocity from the post-collision velocity: \(\displaystyle - \frac{11m}{s}\).
Answer: \(-11\) m/s
(b)
Add both signed stage displacements; the zero-duration event adds none.
The signed contributions 18 and -12 sum to 6 m.
Answer: \(6\) m
(c)
Add speed times duration for each regular stage.
The two positive path lengths sum to 30 m.
Answer: \(30\) m
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Use final minus initial signed velocity, not a difference of speed magnitudes.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: A jump in velocity is not a jump in position.
(b) · 2 marks
- 1 mark: Add both signed stage displacements; the zero-duration event adds none.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Do not assign the vertical graph segment an extra distance or a finite constant acceleration.
(c) · 2 marks
- 1 mark: Add speed times duration for each regular stage.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: A jump in velocity is not a jump in position.
Total: 6 marks.