The Figure Below Shows the Moment When Athletes in the 100-M Sprint Are Crossing the Finishig

2_ch01_SQ_e

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2112001

The figure below shows the moment when athletes in the 100-m sprint are crossing the finishig line. The result of the winner is 10.5 s.

(a) If the time is measured by a hand-held stop-watch, which is accurate to the nearest 0.05 s and the reaction time of human is 0.2 s on average, what is the maximum possible percentage error of the result? (3 marks)

(b) The actual timing device is an electronic timer, which is accurate to the nearest 0.01 s. What is the maximum possible percentage error? (2 marks)

-- ans --

Solutions / Marks
(a) Maximum possible error = 0.2 + 0.2 + 0.05 + 0.05
= 0.5 s / 1A
Maximum possible percentage error = ´ 100% / 1M
= 4.76% / 1A
(b) Maximum possible percentage error = ´ 100% / 1M
= 0.190% / 1A

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2112002

Assume that the Earth travels round the Sun in a circle. Suppose the distance between the Earth and the Sun is R.

(a) Find the magnitude of the displacement of the Earth after 3 months.
(2 marks)

(b) the distance travelled by the Earth after 3 months. (2 marks)

-- ans --

Solution / Marks
(a) The Earth travels a quarter of a circle in 3 months.
/ 1M
Displacement ==R / 1A
(b) Distance travelled =´ 2pR / 1M
=pR / 1A

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2112003

A pendulum swings from X to Y. A student takes a series of photographs of its motion 4 times per second. When he puts the photographs together using a computer software, he gets the following picture.

(a) Find the time needed for the pendulum to swing from X to Y. (2 marks)

(b) What is the displacement of the pendulum when it completes one cycle?
(1 mark)

-- ans --

Solution / Marks
(a) Time needed =´ 4 / 1M
= 1 s / 1A
(b) Zero / 1A

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2112004

A car travels 3000 m forwards and then 1500 m backwards.

(a) What is the total distance travelled by the car? (2 marks)

(b) Take the forward direction as positive. Find the total displacement of the car. (2 marks)

-- ans --

Solutions / Marks
(a) Total distance travelled by the car = 3000 + 1500
= 4500 m / 1M
1A
(b) Total displacement of the car = 3000 + (–1500)
= 1500 m / 1M
1A

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2112005

« A ticker-tape timer is a vibrator that puts black dots on a ticker tape at the rate of 50 dots per second. When an object pulls the tape through the timer, one can trace the motion of the obejct.

A trolley pulls the tape and the tape produced is shown below.

(a) What is the time interval between F and L? (3 marks)

(b) The distance between F and L is 10 cm. Find the average speed of the trolley. (2 marks)

-- ans --

Solution / Marks
(a) Time interval between two adjacent dots == 0.02 s / 1M
\ Time interval between F and L = 5 ´ 0.02
= 0.1 s / 1M
1A
(b) Average speed = / 1M
=
= 1 m s-1 / 1A

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2112006

« A car is travelling at 25 m s–1 initially. Then it accelerates at 3 m s–2.

(a) Find the speed of the car after accelerating for 4 s. (2 marks)

(b) Find the average speed of the car during that 4 s. (2 marks)

-- ans --

Solutions / Marks
(a) By a =, / 1M
3 =
v = 37 m s-1
\ The speed of the car after accelerating for 4 s is 37 m s-1. / 1A
(b) The average speed of the car = / 1M
=
= 31 m s-1 / 1A

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2112007

« The Tsuen Wan Line of MTR is 25.6 km long and it takes 21 minutes and 7 seconds for a train to travel from Central to Tsuen Wan.

(a) Find the average speed of the train. (2 marks)

(b) State two factors that limit the travelling speed of the train. (2 marks)

-- ans --

Solutions / Marks
(a) Average speed of the train = / 1M
=
= 20.2 m s-1 / 1A
(b) Any two of the following:
The maximum acceleration of the train
The maximum deceleration of the train
The maximum speed of the train
The distance between two consecutive stations / 2 ´ 1A

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2112008

« Peter has the following stop-watch.

(a) What is the shortest time interval that Peter’s stop-watch can measure?
(1 mark)

(b) Peter uses his stop-watch to time a falling object and the time recorded is 1.23 s.

(i) The reaction time of human is 0.2 s on average. State the maximum possible error due to reaction time in using the stop-watch. (1 mark)

(ii) Usually experimental results are recorded up to a certain decimal place, depending on the errors occurred in the experiment. What should Peter quote as the result? Explain your answer. (2 marks)

-- ans --

Solutions / Marks
(a) 0.01 s / 1A
(b) (i) Maximum possible error = 0.2 + 0.2 = 0.4 s / 1A
(ii) He should quote the result as 1.2 s. / 1A
This is because the total possible error is 0.4 s, i.e. the measurement is accurate up to 1 decimal place only. /
1A

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2112009

« John and his friends has dinner in a restaurant. The following figure shows how they sit around the table with a turntable of radius 0.5 m.

(a) Wilfred asks Roger for toothpicks. Roger puts them at the edge of the turntable and right in front of him. He turns the turntable until the toothpicks are right in front of Wilfred. What is the distance travelled by the toothpicks? (2 marks)

(b) Roger wants to eat the beef. John turns the turntable until the beef is right in front of Roger. Calculate the magnitude of displacement of the dish of beef. In which direction should John turn the turntable so that it would take the shortest time for Roger to wait? Explain briefly. Assume that the dish is at the edge of the turntable. (4 marks)

-- ans --

Solutions / Marks
(a) Distance travelled by toothpicks = pr
= p ´ 0.5
= 1.57 m / 1M
1A
(b) Magnitude of displacement = / 1M
=
= 0.707 m / 1A
John should turn the turntable clockwise
so that the distance travelled by the dish would be the shortest. / 1A
1A

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2112010

« Tommy walks from point A at the Connaught Road Central to point B where he turns 90° and he finally reaches point C near the Star Ferry Car Park. His route is shown on the map with scale 1:2000. The lengths of AB and BC on the map are
5 cm and 10 cm respectively.

(a) Find the total distance he travelled. (2 marks)

(b) Find his total displacement. (4 marks)

-- ans --

Solutions / Marks
(a) Total distance travelled = (5 + 10) ´ 2000
= 30 000 cm
= 300 m / 1M
1A
(b) Magnitude of displacement = 2000 / 1M
= 22 400 cm
= 224 m / 1A
tan q = / 1M
q = 63.4°
\ Tommy's displacement is 224 m N63.4°W. / 1A

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2112011

« Jane walks from X to Y and then to Z along the path as shown in the following figure.

(a) Calculate the magnitude of displacement of Jane when she travels from

(i) X to Y (displacement d1), (1 mark)

(ii) Y to Z (displacement d2), and (1 mark)

(ii) X to Z (displacement d3). (1 mark)

(b) Is ? Is it always correct no matter where Y is? Explain your answer briefly. (3 marks)

-- ans --

Solutions / Marks
(a) (i) / 1A
(ii) / 1A
(iii) / 1A
(b) / 1A
The equation is not always correct. / 1A
It is correct only if XY and YZ are perpendicular to each other. / 1A

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2112012

« A student uses a digital stop-watch to measure the time taken for a pendulum to swing 2 cycles. The reading is 3.12 s. Assume that the error due to the student’s reaction time was 0.4 s.

(a) Find the percentage error due to the student’s reaction time. (2 marks)

(b) Then the student measures the time taken for 20 cycles and the reading is 27.6 s. What is the new percentage error? (1 mark)

(c) Which result is more accurate, timing 2 cycles or 20 cycles? (1 mark)

-- ans --

Solutions / Marks
(a) Percentage error =´ 100% / 1M
= 12.8% / 1A
(b) Percentage error =´ 100% = 1.45% / 1A
(c) Timing 20 cycles is more accurate. / 1A

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2112013

« In the figure, a marathon runner runs from town A to town D via town B and town C. Use algebraic method to find his total displacement. (4 marks)

-- ans --

Solutions / Marks
AD = / 1M
== 6.32 km / 1A
tan ÐDAE == / 1M
ÐDAE = 18.4°
\ The total displacement is 6.32 km S18.4°W. / 1A

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2112014

« A jumbo jet flies at 260 m s–1 for 10 s. It then flies at 254 m s–1 for 8 s.

(a) Find the total distance it has travelled. (2 marks)

(b) Find its average speed in the journey. (2 marks)

-- ans --

Solutions / Marks
(a) By speed =, / 1M
Total distance travelled = 260 ´ 10 + 254 ´ 8 = 4632 m / 1A
(b) Average speed = / 1M
=
= 257 m s–1 / 1A

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2112015

« A sports car can accelerate from rest to 100 km h–1 in 4.3 s while a motorcycle can accelerate from rest to 80 km h–1 in 3.8 s.

(a) What are the average accelerations of the sports car and the motorcycle?

(3 marks)

(b) If both the sports car and the motorcycle are waiting behind a traffic light, which of them comes up first when the traffic light just turns green? Neglect the reaction time of the drivers. (1 mark)

-- ans --

Solutions / Marks
(a) By a =, / 1M
average acceleration of sports car == 6.46 m s–2 / 1A
average acceleration of the motorcycle == 5.85 m s–2 / 1A
(b) The sports car comes up first. / 1A

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2112016

«« In the following figure, an ant walks from X to Y along the shortest path on a cylindrical block. The radius of the cylindrical block is 0.5 m.

(a) Calculate the distance travelled by the ant as it travels from X to Y.

(Hint: The shortest path between X and Y is a straight line when the curve surface of the cylinder is made flat.) (3 marks)

(b) Calculate the magnitude of the displacement of the ant as it travels from X to Y.

(Hint: The displacement is a line under the curve surface.) (3 marks)

-- ans --

Solutions / Marks
(a) Let s be the distance travelled by the ant.
The arc length between X and Z == m / 1M
Since the shortest path between X and Y is a straight line when the curve surface of the cylinder lies flat, we have
s2 = / 1M
s = 1.27 m
\ The distance travelled is 1.27 m. / 1A
(b) Let d be the magnitude of the displacement.
Straight line between X and Z == 0.707 m / 1M
d 2 = 0.7072 + 12
d = 1.22 m
\ The magnitude of the displacement is 1.22 m. / 1M
1A

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