Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Divide the velocity increase by the first-stage duration.
Worked solution
(a)
Divide the velocity increase by the first-stage duration.
The rising slope is \(\displaystyle \frac{8}{3}\) \(\displaystyle \frac{m}{s^{2}}\).
Answer: \(\displaystyle \frac{8}{3}\) \(\displaystyle \frac{m}{s^{2}}\)
(b)
Use the signed velocity change over the final-stage duration.
The final slope is \(\displaystyle \frac{0- 8}{5}=\)\(\displaystyle - \frac{8}{5}\).
Answer: \(\displaystyle - \frac{8}{5}\) \(\displaystyle \frac{m}{s^{2}}\)
(c)
Calculate the complete area under the nonnegative velocity graph.
Adding the two triangular areas and rectangle gives \(56\) m.
Answer: \(56\) 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: Divide the velocity increase by the first-stage duration.
- 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 graph area is displacement, not acceleration.
(b) · 2 marks
- 1 mark: Use the signed velocity change over the final-stage duration.
- 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 flat nonzero velocity segment represents uniform motion, not rest.
(c) · 2 marks
- 1 mark: Calculate the complete area under the nonnegative velocity graph.
- 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 graph area is displacement, not acceleration.
Total: 6 marks.