Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Apply the zero final velocity to the braking stage only.
Worked solution
(a)
Apply the zero final velocity to the braking stage only.
Set 0=u−bt to obtain \(\displaystyle \frac{16}{5}\) s.
Answer: \(\displaystyle \frac{16}{5}\) s
(b)
Use the signed braking acceleration in the time-free equation.
Using 0=u²−2bD gives \(\displaystyle \frac{128}{5}\) m.
Answer: \(\displaystyle \frac{128}{5}\) m
(c)
Use constant speed during the stated reaction interval.
Unchanged speed times reaction time gives \(32\) m.
Answer: \(32\) 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: Apply the zero final velocity to the braking stage only.
- 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 substitute a positive b as signed acceleration in a forward positive axis.
(b) · 2 marks
- 1 mark: Use the signed braking acceleration in the time-free equation.
- 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: Separate the reaction interval from the braking interval.
(c) · 2 marks
- 1 mark: Use constant speed during the stated reaction interval.
- 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 substitute a positive b as signed acceleration in a forward positive axis.
Total: 6 marks.