Number 5
4 marks · HardA stopwatch measures time in a sprint race as 12.4 seconds, correct to the nearest 0.1 second.
The distance of the race is measured as 100 metres, correct to the nearest metre.
Calculate the upper bound for the runner's average speed in m/s. Give your answer correct to 3 significant figures. (Speed = distance/time)
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
Upper bound speed = maximum distance ÷ minimum time = 100.5 ÷ 12.35 = 8.137 m/s (rounded to 3 significant figures: 8.14 m/s) m/s (±0.01)
Also accept: Full marks for correct bounds and answer to correct accuracy.
Common mistakes: Using wrong bounds (min numerator/max denominator instead of max numerator/min denominator).
Show mark scheme and worked solution
Marking points
M1 · 1 mark · Finds both the lower and upper bounds for both distance and time correctly.
M2 · 1 mark · Recognises to use maximum distance, minimum time for upper bound of speed.
M3 · 1 mark · Correct substitution into the speed formula using bounds.
A1 · 1 mark · Final answer given to 3 significant figures and correct calculation performed. (follow-through)
Worked solution
Lower bound for distance = 100 – 0.5 = 99.5 m; upper bound = 100 + 0.5 = 100.5 m.
Lower bound for time = 12.4 – 0.05 = 12.35 s; upper bound = 12.4 + 0.05 = 12.45 s.
To find the upper bound for speed: use maximum distance and minimum time.
To 3 significant figures: 8.14 m/s.