Motions

When an
object moves from one point (A) to another (B)

we said that the object is in motion .

• •

A B

•
Important terms used in Motion .

1) position :
It . • •

•
is an
object 's location at a certain time .

represented by
"
the letter
"

•
X .

•
measured in a unit of "
m
"
( meter .

•
is a vector quantity .

2) Distance :

It . • •

actual object
•
is the
length covered
by an .

represented by the letter d

" "
• .

•
.
measured in a unit of "
m
"

( meters .

• is a scalar quantity .
3) Displacement :
It • • •

• is the shortest path ( straight line between any two points .

on
is distance in one direction .

represented by of
" "
symbol
"
• the letter X on a
"
DX
I
measured in unit of " "
• a m ( meters . Delta
means the
• is a vector quantity . difference
between
two quantities
•
Displacement is also define as :

The difference between the final and initial position .

Where :

,DJ=Xf-✗i(Lwf
\
Initial position (m )
displacement ( m )
final position (m )

Example # 1 : what is the difference between distance and

displacement ?

Example #2 : An object moves from A to B to C to D ,

as

shown in the
figure below .
Find d- and AI .

A 6m
• •
B

3m

• •
C
D 6m
Example #3 : An object moves from A to B to C ,
as

shown below . Find both d and DX .

o•
A

3km

•
I 4km
B

Example # 4 : An object moves from A to B to C to D and then

come back to A ,
as shown below . Find both d
and DX .

£ 2m
•
B
3m
4m

c•
•

1.5m D

Example #5 : An object moves from A to B to C and then

come back to D , as shown below -

Find both d

and DX covered by the objects .

D A B c
L m • in • ↳

- 7 0 3 6
4)
Velocity : (
Average *elocily )
It . . - .

• is defined as displacement covered over the time taken .

represented by the letter

" "
•
Vav .

unit of meter
'
second)
"
measured
"
m5
"
in
"

• a Mls or ( per

vector
•
is a
quantity . ( It has the same direction as DX ) .

•
Mathematically velocity ,
is
given as :
Final position ( m )
Fisplacement my
(

Initial position em ,
Xf ✗it
m¥aF☐☐¥
-

Average velocity ( tf -

tir-1nil.at time 1st

\ final time (5)
5) Speed : (
Average speed )
It . . .

• is defined as distance covered over the time taken .

represented by the letter

" "
• S .

'
measured unit of
" "
second)
"

•
in a
"
Mls ow m 5 ( meter per .

* is a scalar quantity .

Mathematically .
average speed is given as :

distance em ,

5 =
total distance - § =
deft
Time ( t )
total time taken speed ( miso t.EU
 Example #6 : what is the main difference between J and Vau?

Example # 7 : An object moves from A to B to C as shown in the

figure
below Find the object 's speed and
average average velocity
.
.

• A
Remember :

30s
total distance 3m
g- =

20s
total time
•

I 4m
B

405

Example #8: A boy covered a

displacement of 30m , south in 10s .

Find the boy 's average velocity .

Example # 9: A car moves from A to B and then come back to c

and continues to D as shown below .

and
Find the car's
average velocity average speed .

D • A B
< me • • * an >
2sec 2sec 2sec 2sec
o 5 10
-
go -

g-

Example # 10 : A cheetah is chasing a rabbit that has a

speed of
b- Mls .
If the Cheetah can cover a distance of loom in

12s . Will it be able to catch the rabbit ? Explain .

6) Acceleration :( Acceleration )
Average
It . • .

is defined the
change time interval
• as in
velocity over a .

represented by
"
• the letter air .

• measured in a unit of "

mis
'
"
or
"
m 52 "
( meter per second
squared )
• is a vector quantity .

•
Mathematically ,
average acceleration
is
given as :

change in
velocity
s → Final velocity ( mis)

a =
DV Vf -
Vi -
=
au
Initial
Average acceleration ← ☐t
tf ti -
-

velocity ( mis)
( Mls2)
£ } Initial time is )

change in time final time (s )

•
Average acceleration could be positive negative , ( deceleration ) or even

Zero . As shown below .

up with down with

speeding f- slowing
positive acceleration [ positive acceleration
nyt
+
✗ ✗

yrs speeding acceleration

✓

with up
down
slowing negative
with negative
acceleration
 • Zero acceleration is when the object moving with constant velocity
or
stays at rest ( does not move ) .

Example # 11 : A car is
accelerating from 3m Is to 60 Mls in 20s . find

its acceleration .
( only magnitude)

Example # 12 : A train starts accelerating from rest to a

velocity of

300 m/s ,
North in 150s . Find the train 's acceleration .

and direction )
( magnitude

Example # 13 : An object was

moving with a
velocity of Gomis before it

comes to
stop within 30s .
Find the object's acceleration .

(
only magnitude)

reached final of if
Example # 14 : A tiger a
velocity 6ms in 4s .

the tiger acceleration was 1- miss . Find its initial velocity .

 LX t )
-

.
( v -
t) .
and la t ) -

graphs
R-rated

1. ( position -
time ) graph ( X t)-

✗
dim
• From this
graph we can
get :

1.
Velocity =
slope

→ tis)

2. ( velocity -
time ) graph ( v t)
-
:

V1 Mls )
^
• From this
graph we can
get :

1. Acceleration =
slope
2. Displacement = area under the
graph
>
It 1st

3. ( Acceleration - time )
graph ( a- t ) :

V1
get
a (m.s-2)
Mls )
a
• From this
graph we can :

1. The
change in
velocity = area

under the graph

It 1st
Example # 15 :
According to the
graph below find the
following :

✗ 1m )

:
8 - •

G -
Boo ••

4 -

2- •

•
r n n e i ,⇐• > tls)
1 2 3 4 5 6

between to 3) s
1. The
average velocity -
.

2. The
average velocity between (3-4) s .

between 15 6) s
3. The average
velocity -
.

about the between

4 . What can we
say velocity ( 5- 6) s .

5. The average velocity from lo -

6) s .

6. The
average velocity from 11 -
5) s .

7- The
average speed from ( 1- 5) s .

8. The
average speed from 15 -
6) s .

sketch the and graph of the

object's
9. (v -
E) graph ( a- t)

motion .
Example # 16 :
According to the
graph below find the
following :

1. acceleration between
Average to -71s .

2. Average acceleration between 19 -121s

3. Average acceleration between ( 12 -141s

4. Displacement covered between co -

9) s

5. Displacement covered between ( 9- 161£ .

acceleration
what
say about object's
6 . can we the

between to -71s , 19 -127s ,

and 112-1615 .

7. Instantaneous velocity at 4s

8 .
Average velocity between to -

9) s and ( 9- 161s .
7) Instantaneous speed .

It • . .

• is de find as the speed at a specific time .

• is measured in a unit of "

mis
"
.

• is a scalar quantity .

Mathematically ,
instantaneous speed is
given as :

Si =
¥fl where it should be
as interval ) .
specific not given

or
S; = I V1 til

Instantaneous
8)
velocity .

It • • •

•
is defined as the speed of an object at specific time

and direction . ( instantaneous speed at a

specific directions .

•
is measured in a unit of "
mis
"
.

• is a vector quantity .

Mathematically instantaneous
,
velocity is
given as :

→ displacement as function of time .

d ✗ it,
v ( t) =

dt

• It is much easier to find the instantaneous velocity through graphs ,

it
where is equal to the slope of tangent line at a point on ( ✗ -
t)
graph .
 below find
Example # 17: Through the
graph the
following :

1. Instantaneous velocity at 2sec .

2. Instantaneous speed at 2sec .

3. Instantaneous speed at 4.1sec .

below find
Example # 18 :
Through the
graph the instantaneous velocity
at 2sec and 10sec
9) Instantaneous acceleration .

It • • •

• is defined as the acceleration at specific time .

unit of
"
• is measured in a
"
m 15h .

•
is a vector quantity .

•
Mathematically ,
it is define as :

→ Velocity as a function of time

duct ,
.

a
; =

dt

it
•
Graphically ,
can be found by calculating the slope of tangent line

of a point on a IV t ) -

graph .

below find acceleration

Example # 19 : Through the graph .
the instantaneous

at is 2s , and 3s
,
.
Extra practice :

1. From the graph below find the average velocity between 12 -101s .

below find the instantaneous

2. From the
graph velocity at 1sec and 12sec .

3. Find the instantaneous speed and velocity at 10s ,

6s ,
and 15s .
4 .

According to the graph below find the 1. instantaneous acceleration

at 2s and 4.5s 2. The acceleration between ( o 6. 5) s

average
-
.
.

5. Solve the two questions below .

 sketching (v - t ) and ca t)
-

graphs from

*(x-t)graph•_R
Example # 20 :

Example # 21 :

Baggage
Extra practice :
 t) tha E)
(X
(v
- -

straight
→ step

curved →
2-
~
→
yep

④
→
straight

-
↳
→

L
t
→

E-