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Uniformly accelerated motion
Jun 10, 2025
learn about Uniformly accelerated motion
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0:00
in this video we will deal with
0:01
uniformly accelerated motion most of the
0:05
Motions that we came across in daily
0:07
life is non-uniform motion either things
0:10
are speeding up or they are slowing down
0:14
in non-uniform motion the velocity of
0:16
the body changes as the motion proceeds
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which means the velocity of the body
0:22
keeps changing with the passage of time
0:25
and such a body is set to have
0:27
acceleration now potion with constant
0:30
acceleration or uniformly accelerated
0:33
motion is that in which velocity changes
0:36
at same rate throughout the motion means
0:40
a isal to DV upon DT which is change in
0:44
velocity with the passage of
0:47
time is
0:49
constant now when acceleration of the
0:52
moving object is constant it's average
0:55
acceleration and instantaneous
0:57
acceleration they both are equal so we
1:00
have average
1:02
acceleration equals to instantaneous
1:06
acceleration that is equals to V2 -
1:12
V1 on T2 - T1 where V1 is the initial
1:16
velocity at some time interval T and V2
1:19
is final velocity of the particle at the
1:22
time interval T2 now to discuss further
1:25
let us consider V
1:27
not be the velocity of particle at some
1:31
initial time say T1 = t =
1:36
0 and VB the velocity of particle at
1:40
time
1:41
T2 is equal to
1:44
T now let us number this equation as
1:48
equation one now if we put these values
1:52
in this equation one then we have
1:54
acceleration a = to vus
1:58
V upon T minus t or we have v = v + a t
2:07
let us number this equation as number
2:09
two now this is the velocity time graph
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for reanal motion with constant
2:15
acceleration and from this graph it is
2:17
clear that velocity V at any time T is
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equals to initial velocity plus the
2:25
change in velocity that is 8 so V is
2:28
equals to this velocity V which is the
2:30
initial velocity and change in velocity
2:33
that is equals to 8 which we see here in
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this relation so similarly average
2:38
velocity can also be written as V = to x
2:43
-
2:44
x upon t - 0 where this x not is the
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position of object at time T is equal to
2:51
0 and V this V bar is the average
2:55
velocity between time t equal to 0 to
2:58
time t
3:00
solving this equation for x we get x = x
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+ V T now we know that in interval from
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T is = to 0 to T the average velocity is
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given
3:18
as and now putting this
3:21
equation 2 we
3:26
get and now putting this in equation
3:30
three we
3:51
[Music]
3:54
get and this is the position time
3:57
relation for object moving with
3:59
uniformly accelerated
4:02
motion and now from equation this
4:04
equation five it is clear that an object
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at any time T has quadratic dependence
4:10
on time when it is moving with constant
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acceleration along a straight line and
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position time graph for such a motion
4:19
will be parabolic in nature so this is
4:22
the position time graph of a particle
4:24
moving with uniformly accelerated motion
4:27
now this equation 5 and equation
4:30
are the basic equations of constant
4:32
acceleration and these two equations can
4:34
be combined to get yet another relation
4:37
for x v and a in which we can eliminate
4:40
T now so
4:42
putting T is equal
4:45
to vus V by
4:49
a using this equation
4:52
2 and putting this relation for T in
4:56
equation five and solving for V find
5:00
v² =
5:05
v² + 2 a x -
5:11
x so this is equation 6 now from this
5:14
equation 6 we can clearly see that it is
5:16
a velocity dependent relation between
5:18
velocities of the object moving with
5:21
constant acceleration at time T and T is
5:24
equal to 0 and their corresponding
5:26
positions at that instant of time and
5:29
this
5:30
is and this relation is very useful in
5:33
solving problems when we do not know
5:36
anything about
5:39
time T likewise we can also eliminate
5:43
the acceleration a between equation 2
5:46
and 5 from this relation we have a = to
5:52
v- V upon
5:55
T now putting
5:57
this in equation
6:00
5 we
6:03
get x -
6:07
x is = to v t + 1 by
6:13
2 V - V upon
6:17
T into
6:21
t² so let me label this equation as
6:23
equation number seven and this relation
6:26
is helpful when we do not know about
6:28
acceler
6:29
with which the particle is moving
6:31
similarly we can also eliminate V not
6:34
using equation 2 and 5 so what are
6:37
equations 2 and five they
6:44
are this is equation 2 and the equation
6:48
5
6:51
is now again from equation 2 we have V
6:54
is equal to v- a now putting this
7:00
value of v in equation 5 and solving it
7:02
for x - x we
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find VT - 1X 2 a
7:18
t² so this equation does not involve
7:21
initial velocity th this these basic
7:25
equations 2 5 and derived equations 6 7
7:28
and 8
7:31
then let me
7:39
[Music]
7:41
write so these basic equations 2 five
7:46
and derived equation these 6 7 and 8 can
7:50
be used to solve constant acceleration
7:57
problems now we will discuss what is
7:59
free fall acceleration the freely
8:02
falling motion of any body under the
8:04
effect of gravity is an example of
8:07
uniformally accelerated motion now
8:09
kinematic equations of motion under
8:11
Gravity can be obtained by replacing
8:13
acceleration a in uh the previous
8:17
equations of motion by the letter G
8:21
where G is
8:26
acceleration due to gravity
8:33
and the value of G is equal to
8:38
9.8 m/s squ now chematic equations of
8:43
motion for object moving under the
8:46
action of gravity
8:49
are v = v +
8:53
GT now X = to v t + 1 by 2 GT
9:02
² and V sare - v² equal to 2 g
9:10
x the value of G is taken as positive
9:14
when the body falls vertically downwards
9:17
and its value is taken as negative when
9:19
the body is projected up against the
9:22
gravity so this is all for now in our
9:25
next video we will discuss about
9:27
relative velocity
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