Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Equate the positions or make the relative displacement zero and retain the positive time.
Worked solution
(a)
Equate the positions or make the relative displacement zero and retain the positive time.
The relative displacement is −\(64\)+\(1\)\(\displaystyle t^{2}\). Setting it to zero gives \(\displaystyle t=8 s\).
Answer: \(8\) s
(b)
Evaluate either position at the common meeting time.
A travels \(\displaystyle 5\times 8=40 m\).
Answer: \(40\) m
(c)
Use the elapsed time since B began accelerating.
B has gained aT=\(\displaystyle \frac{16m}{s}\), giving \(\displaystyle \frac{21m}{s}\).
Answer: \(21\) m/s
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: Equate the positions or make the relative displacement zero and retain the positive time.
- 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: Equal velocities alone do not establish a meeting.
(b) · 2 marks
- 1 mark: Evaluate either position at the common meeting time.
- 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: Compare positions at the same physical instant.
(c) · 2 marks
- 1 mark: Use the elapsed time since B began accelerating.
- 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: Equal velocities alone do not establish a meeting.
Total: 6 marks.