Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Add acceleration times elapsed time to the initial velocity.
Worked solution
(a)
Add acceleration times elapsed time to the initial velocity.
Using v=u+at gives \(\displaystyle \frac{19m}{s}\).
Answer: \(19\) m/s
(b)
Include both the initial-velocity and acceleration contributions.
Using s=ut+at²/2 gives \(52\) m.
Answer: \(52\) m
(c)
Use the endpoint-velocity mean only because acceleration is constant.
The constant-acceleration mean of endpoint velocities is \(13\) m/s.
Answer: \(13\) 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: Add acceleration times elapsed time to the initial velocity.
- 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 use one constant acceleration across a force-change event.
(b) · 2 marks
- 1 mark: Include both the initial-velocity and acceleration contributions.
- 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 root from \(\displaystyle v^{2}\) gives a speed unless its direction is restored.
(c) · 2 marks
- 1 mark: Use the endpoint-velocity mean only because acceleration is constant.
- 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 use one constant acceleration across a force-change event.
Total: 6 marks.