analysing linear motion

Forces & Motion SMKSI-mai-06

Name : __________________________________ Form : ___________Date : _____________

LESSON 1 - LINEAR MOTION

A) Introduction

1. Linear motion ___________________________________________________________________ _________________________________.

2. Kinematics _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________.

3. Dynamics _____________________________________________________________________.

4. Distance ,d and Displacement, s

* Distance ,d is ________________________________________________________________ or the length of the path of an object. Distance is __________________ and the value ________________.The unif of distance is ___________________.

* Displacement , s ___________________________________________. Displacement ,s = final position – initial position. Displacement is _______________________ and the value can be positive and negative depend on their directions. The unif of dispacement is ____________

Diagram below shows the difference between distance and displacement.

Distance = Length of the roadDisplacement = Length of the line AB

If the motion in a straight line and in one direction, the magnitude of distance is same as the magnitude of displacement .

5. Speed and Velocity ,v

* Speed is the rate of change of distance.

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Speed = ________________________

Average speed = _________________________

Speed is a scalar quantity and the value always positive. The unif of speed is metre per second (m s-1)

* Velocity is the rate of change of displacement.

Velocity = ______________________

v = s t

Average velocity = __________________________

Velocity is ______________________ and the value can be positive and negative depend on their directions. The unit of velocity is _____________________________________

If an object moves in a circle with constant speed , it has different velocities at different points along the circle because the direction and hence the velocity of the object is always changing as shown in the following diagram.

6. Acceleration,a and Deceleration(Retardation)

* Acceleration is the rate of change of velocity. Acceleration = change in velocity time taken Acceleration = final velocity – initial velocity time taken a = v - u t

Negative acceleration is called as deceleration (retardation). Acceleration is a vector quantity The unif of acceleration or deceleration is metre per second per second (ms-2)

Extra notes 1 uniform = constant = same2 increasing velocity = acceleration3 decreasing velocity (slow down) = deceleration4 zero velocity = the object is stationary (at rest)

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5 negative velocity = the object moves in opposite direction6 uniform velocity = zero acceleration

7 negative acceleration = deceleration (retardation)

Example 1

A boy walks finish the following path AB. Solution

Find(a) total dinstance traveled(b) displacement

Example 2 Solution

Figure above shows runner runs 500 m towards east in 2 minutes and 1200m towards north in 4 minutes. Calculate his(a) average speed(b) average velocity

Example 3

An object accelerates uniformly along a straight line from a velocity of 10 m s-1 until 25 m s-1 in 5 s.Calculate(a) the acceleration of the object(b) the velocity of the object during the first 10 s of motion(c) the time taken to reach a final velocity 50 ms-1

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Solutiona) b)

c)

B) Ticker Timer

1. Using a ticker timer to analyzing the motion

A ticker timer is connected to an alternating electricity supply (a.c.) and uses the mains electricity frequency of 50 Hz to make 50 ticks or vibrations every second. 1 tick is the time interval between one dot and the next dot on the tape.

50 ticks = 1 s 1 tick = 0.02s

Example 4 Solutiona)

Based on the ticker tape above calculate(a) time taken b)(b) average volocity

Example 5

Based on the figure above, calculate the acceleration .

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Solution

Example 6

The figure above shows a ticker tape contains 5 ticks for every interval AB.BC.CD and DE .Calculate

the acceleration.

Solution

Example 7

The following figure shows a tape chart.

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Calcluate(a) the acceleration(b) the average velocity

Solution

a) b)

2. The type of motion based on ticker tape or tape chart (i)

The type of motion is ____________________________________________

(ii)

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The type of motion is

velocity acceleration

(iii)

The type of motion isvelocity acceleration

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(iv)

The type of motion is

velocity acceleration

(v)

The type of motion isvelocity acceleration

C) Using a stroboscopic photograph to analyzing the motion

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Stroboscopic photograph is the taking of very short –exposure pictures of moving objects using a camera and a stroboscope. A stroboscope is a device for making a moving body intermittently visible in order to make appear stationary. The moving object appear ‘freeze’ when the stroboscope frequency at the same frequency of moving object. There are two types of stroboscopes:

(i) Mechanical stroboscope

Stroboscopic photograph frequency = stroboscope frequency x number of slitsor f = np

(ii) Electronic stroboscope ( multiflash stroboscope )

Stroboscopic photograph frequency = light flashes frequency

Example 8

The following figure a stroboscopic photograph shows a metal ball moves along a horizontal plane. The photograph is taken by by using a camera and a mechanical stroboscope rotates with frequency 5 Hz.

(a) State the type of motion of the metal ball.(b) What is the stroboscopic fotograph frequency(c) What is the time intervals between one image and the next.(d) What is the number of images in 30 seconds.(e) Calculate the average velocity of the metal ball

Solution

a) b)

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c) d)

e)

Example 9

The following figure a stroboscopic photograph shows a trolley down an inclined plane. The photograph is taken by using a camera and an electronic stroboscope produces 20 flashes per second.

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(a) State the type of motion of the trolley.(b) What is the stroboscopic photograph frequency(c) What is the time intervals between one image and the next.(d) Calculate

(i) the initial velocity(ii) the final velocity(iii) the acceleration

Solution

a) b)

c) d) i)

ii)

iii)D)Using Equations of Linear Motion with Uniform Acceleration

The various equations of linear motions of an object with uniform acceleration are given as follows:

v = u + at ……………………….(1)

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s = u + v t ………………………..(2) 2

s = ut + ½ at2 ………………………..(3)

v2 = u2 + 2as ………………………..(4)

Where s :_______________________________ u :_______________________________ v :_______________________________ a :_______________________________ t :_______________________________

Extra notes:

moves from rest : ____________________________finally it stops/brakes:____________________________released from a height / fall freely from rest :__________________________thrown vertically upwards:___________________________at maximum height :________________________

Example 10

A car accelerates from rest to 25 m s-1 in 4 s.Find the acceleration of the car.

Solution

Example 1

A bus accelerates uniformly along a straight line from a velocity 20 ms-1 until 30 ms-1 in 5 s. Calculate,(a) the acceleration(b) the total displacement travelled by the bus

Solution a) b)

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Example 12

A construction worker accidentally knocks a brick from a building so that it falls in 4 s to the ground. Calculate(a) the velocity of the brick as it hits the ground(b) the distance fallen of the brick

Solution

a) b)

TUTORIAL 1

1 A car moves with a constant velocity. The acceleration of the car is

A increased B decreasedC zero D uniformly

2 Deceleration means the velocity of an object is

A negative B positiveC increased D decreased

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3 The following figure shows an object moves with a constant speed 5 m s-1 in a circle.The object is also moves with

A an accelerationB zero accelerationC constant velocity

4 The figure shows a path of a moving object.

If AB = 5m , BC = 5m and CD = 7m ,find the total displacement of the object if it moves from A to D.

A 3m B 7mC 13 m D 17 mE 20 m

5 Ali rides a motocycle with a constant speed 30 km j-1 . Bakar runs at a dinstace 100 m in 15 s. Chan rides a bicycle at dinstance 240 km in 10 hours. Which comparison is true?

A Speed of Ali = speed of BakarB Speed of Ali = speed of Bakar = speed of ChanC Speed of Ali > speed of BakarD Speed of Ali =speed of Chan > speed of BakarE Speed of Bakar = Speed of Chan < speed of Ali

6 A tick on the ticker tapes is

A the speed of the ticker timerB the frequency of the ticker timer

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C the dinstace between two consecutive dotsD the time interval between two consecutive dots

7 The frequency of a ticker timer is 50 Hz. The time interval between two consecutive dots is

A 0.60 s B 0.44 sC 0.32 s D 0.30 sE 0.20 s

8 Figure shows the ticker tape for the motion of a trolly.

Which of the following statement is true?

A The volcity between in region DE is same as the velocity in region A B B Frequency in region BC is greater than frekuency in region DEC The time in region AB is same as the time in region DED The velocity between in region CD is low

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Based on the figure above, calculate the average velocity.

A 0.2 ms-1 B 0.3 ms-1 C 0.4 ms-1 D 0.5 ms-1 E 0.5 ms-1

10 What is the average velocity between PQ in the above figure?

A 85 cms-1 B 170 cms-1 B 200 cms-1 C 240 cms-1 E 500 cms-1

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What is the final velocity as shown in figure above?

A 40 cms-1 B 120 cms-1 C 150 cms-1 D 267 cms-1 E 420 cms-1

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Based on the figure above , calculate the acceleration.A 2 ms-2 B 4 ms-2 C 5 ms-2 D 8 ms-2 E 10 ms-2

14 Based on the figure above , calculate the acceleration.

A -5 ms-2 B - 50 ms-2 C - 500 ms-2 D 50 ms-2 E 500 ms-2

15 The following figure shows a tape chart.

Based on figure , which of the following is true?

At the beginning of motion At the end of motionA the velocity unchanged the acceleration increasesB the velocity increases the acceleration increasesC the velocity increases the acceleration unchangedD the velocity unchanged the acceleration unchanged

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16 Which of the following shows an object moving with decreasing acceleration ?

17 The following figure is a stroboscopic photograph shows a ball moves on a smooth table. Which of the following is true?

A The acceleration is constantB The velocity is increasingC The acceleration is zeroD The velocity is zero

18 A stroboscope has 4 slits and rotates with frequency 5 Hz. The time intervals between two successive images is

A 40.0 s B 2.0 sC 1.0 s D 0.4 sE 0.05 s

19 The following figure a stroboscopic photograph shows an ice cube moves along a horizontal plane. The photograph is taken by using a camera and a mechanical stroboscope has 2 slits and rotates with frequency 25 Hz.

What is the velocity of the ice cube?

A 5 cms-1 B 25 cms-1C 100 cms-1 D 250 cms-1E 500 cms-1

20 The following figure a stroboscopic photograph shows a ball moves along a horizontal plane. The photograph is taken by by using a camera and an electronic

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stroboscope produces 50 flashes per second.

Calculate the average velocity of the ball.

A 0. 5 ms-1 B 1.0 ms-1C 1.5 ms-1 D 2.0 ms-1E 3.0 ms-1

21 The following figure a stroboscopic photograph shows a boy down an inclined plane. The photograph is taken by using a camera and an electronic stroboscope produces 4 flashes per second.

The acceleration of the boy is

A 6ms-2 B 12 ms-2

C 24 ms-2 D 32 ms-2

E 48 ms-2

22 A cyclist riding at a velocity 8 ms-1 and is accelerating with 4 ms-2 . What is the velocity of the cyclist after 5 s .

A 16 ms-1 B 20ms-1 C 24 ms-1 D 28 ms-1

E 32 ms-1

23 A rocket starts at velocity 2500 ms-1 and accelerates uniformly upwards at 20 ms-2 . What is the velocity of the rocket after 4 minutes.

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A 4800 ms-1 B 5000 ms-1 C 6800 ms-1 D 7300 ms-1

E 7500 ms-1

24 A trolley starts from rest and is uniformly accelerated to speed of 12 cms-1 in 5 . What is the distance traveled by the trolley?

A 16 cm B 24 cmC 28 cm D 30 cmE 42 cm

25 A car starts from rest and accelerates uniformly and after travels at distance 45m the velocity of the car is 20 ms-1 . What is the time taken?

A 4.5 s B 9.0 sC 13.5 s D 18.0 sE 22.4 s

26 A airplane accelerates at 40 ms-2 in 10 s to take off. What is the minimum length of the runway on the airfield?

A 1000 m B 2000 mC 3000 m D 4000 m

E 5000 m

27 A car starts from rest and accelerates uniformly . If the distance reached is 900 m after travels in 30 s, calculate the acceleration of the car.

A 5 ms -2 B 4 ms-2 C 3 ms-2 D 2 ms-2 E 1 ms-2

28 A lorry start from rest and accelerates at 10 ms-2. What is the velocity of the lorry after travels for a distance 20m ?

A 10 ms-1 B 20ms-1 C 40 ms-1 D 80 ms-1

E 100 ms-1

29 A car travels with a velocity 15 ms-1 . It then accelerates uniformly and travels a distance of 12.5 m. If the velocity reached is 10 ms-1 find the acceleration of the car.

A –5.0 ms-2 B –2.5 ms-2 C 2.5 ms-2 D 5.0 ms-2

E 7.5 ms-2

30 A car moves with a velocity 40 ms-1 . After the brakes of the car is applied ,it moves 100 m more before coming to rest. Calculate the deceleration of the car.

A 4 ms-2 B 8 ms-2

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C 12 ms-2 D 16 ms-2 E 20 ms-2

31 A lorry moves with a velocity 20 ms-1. After the brakes of the car is applied it moves for a distance 4 m before coming to rest. What is the time taken before it stops?

A 10 s B 8 sC 6 s D 4 sE 2 s

32 A stone fall freely from rest through a height of 5 m. What is the velocity of the stone when it hits the ground.

A 5 ms-1 B 10 ms-1 C 15 ms-1 D 20ms-1 E 30 ms-1

33 A coconut falls vertically to the ground. If the coconut takes 1.5 s to fall to the ground, calculate the height from which it fell.

A 8.45 m B 11.25 mC 15.00 m D 22.50 m

E 31.25m

34 A metal sphere falls 125m vertically to the ground. What is the time the metal sphere takes to reach the ground?

A 2 s B 4sC 5 s D 8sE 10 s

35 A ball is thrown vertically upwards from the ground with a velocity of 20 ms-1. Calculate the maximum height reached.

A 60 m B 40 mC 30 m D 20 mE 10 m

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36 The table (a) and (b) shows the distances traveled and the times taken for four students in a competition

Student Distance/m Time/ sP 100 20Q 120 20

Table (a)

Student Distance/ m Time/ sR 100 20S 100 15

Table (b)

(a) Compare the speeds of the

(i) student P dan student Q

(ii) student R dan student S

(b) State the relationship between

(i) the speed and the distance in table (a)

(ii) the speed and the distance in table (b)

(c) Based on the relationship in (b),state the definition of speed.

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38 The following figure shows a tape chart . The chart is produced by the motion of a trolly.The ticker timer used a supply voltage 12 V a.c. at 50 Hz.

(a) Describe the type of motion is shown in the tape chart.

(b) What ishe time interval between two consecutive dots ?

(c) Calculate

(i) the minimum velocity

(ii) the maximum velocity

(iii) the average velocity.

(iv) the acceleration.

39 The following equation shows the equations of linear motion of an object with uniform acceleration. v = u + at

(a) (i) What is meant by the symbol of ‘a’

(ii) Give the definition of the symbol of ‘a’

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(b) (i) What is the information can you get from the term of ‘at’

(ii) What is the S.I. units for the term of ‘at’

(c) The above equation can also be used for an object in state of free-fall. A stone fall freely to the ground from rest in 4 s.(i) What is meant by ‘fall freely’?

(ii) Calculate the velocity of the stone when it hits the ground.

40 Each figure below shows two positions of a student on a swing. The initial position in each figure is different.

Observe the positions of each of the swing in each diagram and the appearance of the student when she swings. Based on the observations:

(a) State one suitable inference that can be made. (b) State one appropriate hypothesis for an investigation.(c) With the use of apparatus such as trolley, ticker timer and other apparatus, describe an

experimental framework to test your hypothesis. In your description, state clearly the following:

(i) Aim of the experiment(ii) Variables in the experiment(iii) List of apparatus and materials(iv) Arrangement of the apparatus

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(v) The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable.

(vi) Way you would tabulate the data (vii) Way you would analysis the data

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analysing linear motion

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