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2.1 Linear Motion

Introduction

               

           Linear motion is the motion  a straight line and 

the movement  in a direction where forwards is positive

and backwards is negative.

Kinematics is the section of physics which studies the

motions of  objects without considering the effects that produce the motion. The study generally involves the analysis of the position of an object in relation to time.

Dynamics  is the section of physics which studies the

causes of motion of an object.

 

Distance ,d and Displacement, s

 

Distance ,d is how far a body travels during a motion

without  considering  any particular direction or the length of the path of an object.

Distance is a scalar quantity  and  the value always positive.

The unif of distance is metre (m)

 

Displacement , s  is distance traveled in a particular direction.

Displacement ,s = final position – initial position

Displacement is a vector quantity  and  the value can be positive and negative depend on their directions.

The unif of dispacement is metre (m)

               

          Diagram below shows the difference between distance

and  displacement.

clip_image002

                Distance = Length of the road

                Displacement = 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 .

                Speed and Velocity ,v

                Speed is the rate  of change of distance.

                                Speed = distance travelled

                                                   time taken

 

                Average speed = total distance traveled

                                                    total time taken

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 = displacement

                                                    time taken

                                                  v = s

                                                       t             

                Average velocity =  total displacement

                                                   total time taken

 

Velocity is  a vector quantity  and  the value can be positive and negative depend on their directions.

The unif of velocity is metre per second (m s-1)

               

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.

clip_image004

               

Acceleration,a  and Decelaration(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 = same

                2              increasing velocity = acceleration

                3              decreasing velocity (slow down) = deceleration

                4              zero velocity = the object is stationary (at rest) 

                5              negative velocity = the object moves in opposite direction    

                6              uniform velocity = zero acceleration

                7    negative acceleration =  deceleration

        (retardation)

Example  1

 

A boy walks  finish  the following path AB.

clip_image006

Find

(a)       total dinstance traveled

(b)       displacement

 

                Solution

 

Example 2


clip_image007


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

 

Solution

 

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

 

Solution

 

 

                Using a ticker timer to analysing 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

 

clip_image008

                Based on the ticker tape above        calculate

                (a)           time taken

                (b)           average volocity

 

Solution

Example  5

 


clip_image010


                Based on the figure above, calculate the acceleration .

 

Solution

 

Example  6

 

 

clip_image012
The figure above shows a ticker tape contains 5 ticks for every interval AB.BC.CD and DE .Calculate the acceleration.

 

Solution

 

 

 

 

Example 7

clip_image014

The following figure shows a tape chart.

Calcluate

(a)                 the acceleration

(b)                 the average velocity

 

Solution

 

 

The type of motion based on ticker tape or tape chart

 (a)

The type of motion is 


clip_image015


 

clip_image016velocity

acceleration

 

constant

zero

 

(b)

 

clip_image018
The type of motion is

 

velocity

acceleration

increase

 

constant

(c)


clip_image020


                The type of motion is

velocity

acceleration

increase

 

constant

 

 

(d)


clip_image022


The type of motion is

 

velocity

acceleration

Increase

constant

 

(e)

 

clip_image024
                The type of motion is

velocity

acceleration

decrease

deceleration

 

 

Using a stroboscopic photograph to analysing the motion

 

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


clip_image026


                                Stroboscopic fotograph frequency = stroboscope    

                                      frequency  x   number of  slits                    

 

or            f = np

 

                (ii)           Electronic stroboscope ( multiflash stroboscope )


clip_image028


                 

Stroboscopic fotograph 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)     

clip_image029


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

 

 

Example  9

 

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

clip_image031 

(a)         State the type of motion of the trolly.

(b)         What is the stroboscopic fotograph 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

 

 

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)

clip_image002………………………..(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

 

 

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

 

2 Responses

  1. Kenapa tiada solution?

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