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Average velocity and speed
Jun 10, 2025
In this tutorial learn about average speed and average velocity
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0:01
in our last video we had talked about
0:03
position distance and displacement and
0:06
we also note that simplest motion to
0:09
describe is motion of a point along a
0:11
straight line
0:13
which we shall take to coincide with the
0:15
coordinate axis now in our this video we
0:18
will talk about average velocity and
0:20
speed
0:22
now we all know that
0:25
speed
0:28
is equals to distance
0:33
traveled
0:35
upon time taken
0:41
now this is the basic definition of
0:43
speed
0:44
now for discussing it further consider a
0:47
particle moving along a straight line
0:50
along x axis
0:52
x coordinate describing motion of the
0:54
particle from origin o varies with time
0:57
or we can say that x coordinates depend
0:59
on time
1:05
now consider this figure if at any time
1:08
t1 particle is at point p and at a
1:11
distance x1 from the origin and at time
1:13
t2 it is at point q at a distance x2
1:16
from the origin
1:18
then displacement during this time
1:20
interval is vector from point p to q and
1:23
is given as
1:28
delta x is equals to x 2
1:31
minus
1:32
x 1
1:34
now average velocity of the particle is
1:36
defined as the ratio of the displacement
1:39
that is delta x of the particle in the
1:41
time interval delta t which is equals to
1:49
e2 minus t1 mathematically it is written
1:52
as v is equals to delta x upon delta t
1:56
now consider this figure
1:58
this figure represents the coordinate
2:00
time graph of the motion of the particle
2:03
that is it shows how the value of x
2:05
coordinate of moving particle is
2:08
changing with the passage of time
2:10
now in this figure average velocity of
2:12
the particle is represented by the slope
2:16
of odd pq
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which is equal to the ratio of
2:22
displacement delta x occurring in the
2:25
particular time interval delta t now
2:28
like displacement average velocity
2:32
we also has magnitude as well as
2:35
direction
2:37
or we can say that this average velocity
2:40
is a vector quantity average velocity of
2:43
the particle can be positive as well as
2:46
negative and its positive and negative
2:48
values depends upon the sign of
2:51
displacement
2:52
if displacement of the particle is zero
2:55
then average velocity is also equals to
2:57
zero so position time graph of a
2:59
particle moving with positive average
3:01
velocity is like this
3:06
positive average velocity
3:09
and graph for particle moving with
3:12
negative average velocity
3:15
would be of the form
3:18
like this
3:25
and if a particle is at rest
3:28
then graph would be of the form just
3:31
like this means there is no change in
3:33
position with the passage of time
3:36
so for positive average velocity slope
3:38
of the line
3:40
slides upwards
3:43
right or we can say that it has positive
3:45
slope
3:46
and for negative average velocity slope
3:49
line
3:50
slants
3:52
down to the right that is it has
3:55
negative slope and for particle address
3:57
slope is zero
4:00
now displacement of the object is
4:02
different from the actual distance
4:04
travelled by the particle
4:06
so for actual distance traveled by the
4:08
particle its average speed is defined as
4:11
the total distance travelled by the
4:13
particle in the time interval during
4:15
which the motion takes place so
4:17
mathematically
4:19
average speed
4:21
is equals to total distance
4:23
divided by total time interval since
4:26
distance traveled by a particle does not
4:28
involve direction so speed of the
4:30
particle depending on distance traveled
4:33
does not involve distance and hence it
4:35
is the vector quantity and is always
4:38
positive
4:42
of average speed may differ from average
4:44
velocity because in case of motion with
4:47
average speed distance may be greater
4:50
than the magnitude of displacement
4:53
and this can be cleared with the help of
4:55
an example
5:22
now
5:23
consider this figure
5:25
now
5:26
here a man starts travelling from origin
5:29
till point q
5:30
and return to the point p then in this
5:33
case displacement of the man is from
5:39
o
5:40
to q
5:41
which is equals to
5:43
80 meter
5:48
and displacement from
5:52
q
5:53
to p
5:56
is equals to
5:58
20 minus 80
6:00
that is equal to minus 60
6:03
meter
6:04
now total displacement of the particle
6:06
in moving from point o to q and then
6:09
from point q to p
6:11
now total displacement of the particle
6:13
in moving from point o to q
6:16
and then from point q to p is equals to
6:20
80
6:25
20
6:26
is equal to 20 meter now the total
6:29
distance travelled by the map
6:32
from
6:32
oq
6:34
to
6:35
qp
6:36
is equals to
6:38
80 plus 60 is equal to 140
6:42
meters now from this we can say that
6:45
average speed
6:47
depending on the distance is in general
6:49
greater than the magnitude of velocity
7:00
so this is all for now and in our next
7:02
video we will discuss about
7:04
instantaneous velocity
7:06
speed
7:09
and acceleration
#Primary & Secondary Schooling (K-12)