Std ver Mech01 Kinematics s4 - · PDF fileA ball rolling along a circular track with constant...

New Senior Secondary Physics Compulsory: Mechanics Chapter 1 Kinematics

CHAPTER 1KINEMATICS

1 Scalars and Vectors

[Concept] [HKCEE] Which of the following is/are vectors? (1) momentum (2) kinetic energy (3) potential difference A. (1) only B. (2) only C. (1) and (3) only D. (2) and (3) only E. (1),(2) and (3) Concepts of scalars and vectors

2 Position and speed

Distance vs Displacement


[Concept] Example 1: Peter travels 10m due North, 10 m due East and then 10 m due South. (a) What are his distance and displacement in the whole trip?

Speed vs Velocity (b) If Peter used 6s to complete his trip, what are his average speed and velocity over the whole trip?

Average vs Instantaneous (c) If Peter used 1s to run his first part (due North), 2s for 2nd part (due East) and 3s for 3rd part (due South), what are his instantaneous speeds and velocities in each part of his trip?


Graphs of motion (d) Sketch the graphs of (i) distance travelled against time and (ii) speed against time for Peter’s trip. [Further question 1: Can the distance travelled becomes negative?] [Further question 2: Can we sketch the graph of displacement against time in this case?]

[Concept] [HKCEE] A man takes 30 s to walk 80 m towards the east. He then takes 10 s to run 60 m towards the south. Which of the following statements is/are correct? (1) The magnitude of the resultant displacement of the man is 140 m (2) The average speed of the man is 4.3 ms-1

(3) The magnitude of the average velocity of the man is 2.5 ms-1

A. (1) only B. (3) only C. (1) and (2) only D. (1) and (3) only E. (1) ,(2) and (3) [Further question: What is the average velocity of the man over the whole trip?]


[Calculation] [HKCEE] A man walks 40 m towards the west. He then walks 40 m toward the south and lastly walks 70 m towards the east. Find the magnitude of the resultant displacement of the man. A. 30m B. 40m C. 50m D. 70m E. 150m

Displacement-time graph and velocity-time graph Example 2: Mary walks to the right by 80m in 40s, she then takes a rest for 10s and then walks backward by 30m in 20s. Taking right as positive, sketch the following graphs for Mary’s trip: (i) Distance-time graph (ii) Displacement-time (s t− graph) (iii) Speed-time graph (iv) Velocity-time (v t− graph)


[Graph reading] [HKCEE]

The figure above shows the distance-time graphs of two toy cars P and Q moving along a linear track. They start at the same point. Which of the following statements are correct? (1) Car P will reach the 20 m-mark first. (2) Car P is overtaking car Q at t = 5 s. (3) The average speed of car P in the first 5 s is smaller than that of car Q. A. (1) and (2) only B. (1) and (3) only C. (2) and (3) only D. (1), (2) and (3)

Brief Summary


3 Acceleration

[Concept] Which of the following conditions refers to objects moving with acceleration? I. A girl walking on a street along a straight line with constant speed. II. A ball falling freely under gravity. III. A car starts from rest and moving faster and faster. IV. A ball rolling along a circular track with constant speed.

Concept of acceleration

Unit of acceleration

[Changing unit] [HKCEE] A racing car accelerates from rest to a speed of 100 km h-1in 3.2 s. Find the average acceleration of the car. A. 4.34 ms-2

B. 8.68 ms-2 C. 15.63 ms-2

D. 31.25 ms-2 E. 112.50 ms-2


[Simple acceleration] Example 3: A dog start running from rest along a straight line. It accelerates uniformly at -22 ms for 5s. (a) Find the speed of the dogat 5st= .

(b) Sketch the (i) a t− (ii) v t− and (iii) s t− graphs of the dog.


[Accelerate and then decelerate] Example 4: A car accelerates uniformly from rest along a straight road for 7s at -25 ms . It then travels with uniform speed for 4s. After that the driver applies a brake so that the car decelerates uniformly to stop by 6s. (a) Find the speed of the car at 7st= .

(b) Find the acceleration of the car during braking.

(c) Sketch the (i) a t− (ii) v t− and (iii) s t− graphs of the car


[Graph reading] [HKCEE] The above diagram shows the variation of the acceleration of an object which is initially at rest. Which of the following velocity-time graphs correctly describes the motion of the object?

[Graph reading] [HKCEE] A car starts from rest and travels along a straight road. The acceleration-time graph of the car is shown above. Which of the following graphs shows the variation of the velocity v of the car with time t?



Two cars A and B travel along the same straight road. The velocity-time graphs of the two cars are shown above. Which of the following statements about the motion of the two cars at time T0 is/are always correct? (1) The two cars meet each other (2) The two cars are moving with the same speed but in opposite directions (3) Car A is accelerating while B is decelerating A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1),(2) and (3)


The above diagram shows the variations of the velocity of an object with time. What is the distance travelled by the object in the first 3 seconds? A. 5m B. 15m C. 25m D. 30m E. 45m

New Senior Secondary Physics CompulsoryChapter 1 Kinematics


A car is traveling at a uniform speed of 10 m sbring the car to rest with uniform deceleration. Figure 1 shows the speedfrom the instant the driver first sees the signal. (a) Write down the reaction time of the driver, i.e. the apply the brakes. (1 mark) (b) Find the area under the graph in Figure 1. State its physical meaning. (4 marks)

Compulsory: Mechanics

Figure 1A car is traveling at a uniform speed of 10 m s–1. The driver sees a warning signal and applies the brakes to bring the car to rest with uniform deceleration. Figure 1 shows the speed-time graph of the car, starting from the instant the driver first sees the signal.

(a) Write down the reaction time of the driver, i.e. the time lapse between seeing the signal and starting to

(b) Find the area under the graph in Figure 1. State its physical meaning. (4 marks)

Figure 1 warning signal and applies the brakes to

time graph of the car, starting

time lapse between seeing the signal and starting to

(b) Find the area under the graph in Figure 1. State its physical meaning. (4 marks)


(c) If there is an obstacle 20 m ahead when the driver first sees the signal, would the car hit the obstacle? Explain your answer. (2 marks) (d) Assume that the reaction time of the driver and the deceleration of the car remain unchanged.

(i) In Figure 1, draw a speed-time graph for the car if it is initially traveling at 20 m s–1. (ii) A student says ‘if the initial speed of the car is doubled, the stopping distance of the car would be

doubled.‘ State whether his statement is true or false and explain briefly. (6 marks)


[Describe motion] [HKCEE] A boat starts from rest at time t = 0 s and travels along a straight line. Figure 1 shows the velocity-time graph of the boat from t = 0 to 300 s. Describe the motion of the boat from t = 0 to 300 s. (5 marks)

FINAL REMARKS

The main idea of this chapter is to develop a set of tools to describe motion, while we suppressed the question of “how the motion was formed?” at the moment. We introduced the concepts of distance/displacement, speed/velocity and acceleration for describing motion, while these quantities naturally falls into scalars or vectors.

We then introduced s t− , v t− and a t− graphs to describe complicated motions, and graph reading is the most important technique students have to master in this chapter. Students should always bear in mind the slope and area relationships between the three graphs. However, students should not forget that these graphs are applicable for motion in 1 dimension only where we use (+) and (-) sign to denote directions along the line. We cannot plot vector quantities directly for 2 or more dimensional problems.

Although some calculation was involved in this introductory chapter in kinematics, we intentionally suppressed all formal mathematical equations until chapter 2. Students are expected to get a strong understanding on each concept in this chapter, which they constitute the foundation for all further treatment in mechanics. In chapter 2, we will present all the mathematical equations concerning uniform accelerated motion in 1 dimension.

In terms of examination skills, students should most aware about the slope and area relationship and how to describe motion from a given motion graph.


APPENDIX 1 TIME MEASUREMENT AND ERROR TREATMENT

Time measurement: Stop watchand error treatment [Error treatment] [HKALE] In an experiment to determine the period of oscillation, T, of a simple pendulum, the time, t, for a number of complete oscillations is taken. It is found that the time for 30 complete oscillations is 28.7 ± 0.3 s. Which of the following statements is/are correct? (1) The reading error in t can be reduced by counting 50 oscillations. (2) The percentage error in T is the same as that in t. (3) The period T determined should be quoted as 0.96 ± 0.01 s. A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only E. (1), (2) and (3)


Speed/acceleration measurement: Stroboscopic Lamp [Stroboscopic Lamp] [HKCEE] An object travels with uniform deceleration along a track.

Figure 2 shows a strobe photograph of the object as it travels. The stroboscopic lamp is flashing at a frequency of 5 Hz. Find the deceleration of the object. (4 marks)

Speed/acceleration measurement: Light Gate [Light Gate] [HKCEE]


APPENDIX 2 AVERAGE SPEED VS SIMPLE AVERAGE

Speed/acceleration measurement: Stroboscopic Lamp [Concept] A car travels directly from city A to city B at 30 -1ms . It returns immediately to city A at 20 -1ms . The distance between the cities is 600m. Find the average speed of the car over the whole journey. [Further question] Is the distance 600m important?

Std ver Mech01 Kinematics s4 - · PDF fileA ball rolling along a circular track with constant...

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