Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Subtract the original velocity from the final velocity and divide by elapsed time.
Worked solution
(a)
Subtract the original velocity from the final velocity and divide by elapsed time.
The signed change -5 divided by 2 gives \(\displaystyle - \frac{5}{2}\) \(\displaystyle \frac{m}{s^{2}}\).
Answer: \(\displaystyle - \frac{5}{2}\) \(\displaystyle \frac{m}{s^{2}}\)
(b)
Take the magnitude of this negative acceleration only after interpreting the motion.
Both velocities are positive and speed decreases, so the deceleration magnitude is \(\displaystyle \frac{5}{2}\).
Answer: \(\displaystyle \frac{5}{2}\) \(\displaystyle \frac{m}{s^{2}}\)
(c)
Convert kilometres to metres and hours to seconds.
Divide 72 by 3.6 to obtain \(20\) m/s.
Answer: \(20\) 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: Subtract the original velocity from the final velocity and divide by elapsed 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: A negative acceleration does not always imply decreasing speed.
(b) · 2 marks
- 1 mark: Take the magnitude of this negative acceleration only after interpreting the motion.
- 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: Convert both velocity readings to the same units before subtraction.
(c) · 2 marks
- 1 mark: Convert kilometres to metres and hours to seconds.
- 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 negative acceleration does not always imply decreasing speed.
Total: 6 marks.