introduction of mechanics lecture notes 2 for students

8/14/2019 Introduction of Mechanics Lecture Notes 2 for Students

1/27

Introduction of mechanics

Lecture notes 2

Displacement time graph Velocity time graph

Acceleration time graph

Equations of motion Acceleration due to gravity

Free fall

Free fall motion with a change in direction


2/27

A displacementtime graphor stgraph ( )

1 Displacementtime graph

shows the displacement of amoving object at different times.


3/27

Consider: A car is travelling at aconstantor uniformvelocity of 10m s1.

movesmoves 1010

mm every 1 severy 1 s


s / m

t/ s0 41 2 3

10

20

30

40


4/27


The slope of the s tgraphgives the velocity of the body.

slope =

s

tt1 t2

s1

s2 s2s1

t2t1= velocity

Slope ofs tgraph


5/27

A velocitytime graphor v t

graph( )

2 Velocitytime graph

gives the velocity of a moving

object at different times.


6/27

The v tgraphfor the car travellingat a constantvelocity of 10 m s1:

v/ m s1

t/ s

1

0a horizontal line:the velocity staysthe same all thetime.



7/27


The slope of the v tgraph gives

the acceleration of the body.

v

tt1 t2

v2

v1

slope =v2v1

t2t1

= acceleration

a Slope of v tgraph


8/27

The v tgraph isa horizontal line

the car istravelling at a

constant velocity with noacceleration

it has a zeroslope

a Slope of vtgraph

v/ m s1

t/ s

10


9/27

b Area under vtgraph

The area under a v tgraph is the

displacement (s) during the time interval.

v

t0

This area= displacement

t

v


10/27

The accelerationtime graphor atgraph( )

3 Accelerationtime graph

gives the acceleration of thecar at different times.


11/27

The a tgraphfor the cartravelling at a constantvelocity of10 m s1:

a / m s2

t/ s

Acceleration = 0 ms2

3 Accelerationtime graph

The graph is exactly zero allthe time,since the car is moving atconstant velocity: zero

acceleration.


12/27

4 Graphs for uniformly accelerated motion

Consider a car speeding up.

a Uniformly accelerated motionalong a straight line


13/27

a Uniformly accelerated motion

along a straight line

area = vt2

slope = v/t


14/27

a Uniformly accelerated motion

along a straight line

s tgraph

v tgraph

a tgraph

slope

slope

area


15/27

b Uniformly accelerated motion

with a change in direction

If the acceleration and the

initial velocity point in oppositedirection is,

what do the motion graphs look

like?


16/27

b Uniformly accelerated motion with a

change in direction

If the acceleration and theinitial velocity point in oppositedirection is,


17/27

1 Equations of motion for

uniform accelerating objects

s : displacement

t : time duration

u : initial velocity v : final velocity

a : acceleration

v= u + at

2

1s = ut+ at2

v2 u 2 = 2as

2

(u + v)t

s =


18/27

Blackbird (Lockheed SR-71A) wasthe fastest jet in the world

Example 1

Its max. speed

is 894 m s1andits max.acceleration is

3.75 m s2.Estimate the shortest distance it travelledwhen it accelerates from the rest to its

top speed.


19/27

Example 1

Its max. speed is 894 m s1and its max.acceleration is 3.75 m s2.

Estimate the shortest distance ittravelled when it accelerates from therest to its top speed. Answer:

u = 0 , a = 3.75, v = 894 , s = ?

V 2 = u 2 + 2 a s

8942= 0 + 2 (3.75) s

s = 106564.8 m


20/27

If resistance is negligible,

Accepted value = 9.8 m s2

2 Acceleration due to gravity

a body falls freely under gravitywith uniform acceleration.

acceleration due togravity, g

Take g 10 m s2 for simplicity.


21/27

2 Acceleration due to gravity

a Free fall

If a ball is dropped from 20 m


22/27

a Free fall


23/27

b Free fall motion with a change

in direction

If a ball is thrown verticallyupwards with v= 30 m s1


24/27

b Free fall motion


After it reaches the highestpoint


25/27

b Free fall motion



26/27

b Free fall motion



27/27

introduction of mechanics lecture notes 2 for students

Documents