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Hello students, here in this video we are going to learn a very important Topics as, UNIFORM MOTION, AVERAGE SPEED, AVERAGE VELOCITY from class 11th physics.
What is motion? How do we understand Distance? What are distance and displacement? Is Displacement the same as Distance? Watch this video to know more!
When an object is in motion, its position
changes with time. But how fast is the position
changing with time and in what direction? To
describe this, we define the quantity average
velocity. Average velocity is defined as the
change in position or displacement (Δx) divided
by the time intervals (Δt), in which the
displacement occurs :
The SI
unit for velocity is m/s or m s–1, although km h–1
is used in many everyday applications.
Like displacement, average velocity is also a
vector quantity. Geometrically, this is the slope of the straight
line P1P2 connecting the initial position P1 to
the final position P2 It
is zero if the displacement is zero.
It
is zero if the displacement is zero.Average speed has obviously the same unit
(m s–1) as that of velocity. But it does not tell us
in what direction an object is moving. Thus, it
is always positive (in contrast to the average
velocity which can be positive or negative). An object is said to be in motion if its position changes with time. The position of the
object can be specified with reference to a conveniently chosen origin. For motion in
a straight line, position to the right of the origin is taken as positive and to the left as
negative.
2. Path length is defined as the total length of the path traversed by an object.
3. Displacement is the change in position : Δx = x2 – x1. Path length is greater or equal to
the magnitude of the displacement between the same points.
4. An object is said to be in uniform motion in a straight line if its displacement is equal
in equal intervals of time. Otherwise, the motion is said to be non-uniform.
5. Average velocity is the displacement divided by the time interval in which the
displacement occurs :
v
x
t
=
Δ
Δ
On an x-t graph, the average velocity over a time interval is the slope of the line
connecting the initial and final positions corresponding to that interval.
6. Average Speed is the ratio of total path length traversed and the corresponding time
interval.
The average speed of an object is greater or equal to the magnitude of the average
velocity over a given time interval.
7. Instantaneous velocity or simply velocity is defined as the limit of the average velocity as
the time interval Δt becomes infinitesimally small :
d
t 0 t 0 d
x x
v lim v lim
Δ → Δ → t t
= = Δ =
Δ
The velocity at a particular instant is equal to the slope of the tangent drawn on
position-time graph at that instant.
8. Average acceleration is the change in velocity divided by the time interval during which
the change occurs :
v
a
t
= Δ
Δ
9. Instantaneous acceleration is defined as the limit of the average acceleration as the time
interval Δt goes to zero :
d
t 0 t 0 d
v v
a lim a lim
Δ → Δ → t t
= = Δ =
Δ
The acceleration of an object at a particular time is the slope of the velocity-time
graph at that instant of time. For uniform motion, acceleration is zero and the x-t
graph is a straight line inclined to the time axis and the v-t graph is a straight line
54 PHYSICS
parallel to the time axis. For motion with uniform acceleration, x-t graph is a parabola
while the v-t graph is a straight line inclined to the time axis.
10. The area under the velocity-time curve between times t1 and t2 is equal to the displacement
of the object during that interval of time.
11. For objects in uniformly accelerated rectilinear motion, the five quantities, displacement
x, time taken t, initial velocity v0, final velocity v and acceleration a are related by a set
of simple equations called kinematic equations of motion :
v = v0 + at
x v t
1
2
0 at
2 = +
v v 2ax 2
0
2 = +
if the position of the object at time t = 0 is 0. If the particle starts at x = x0 , x in above
equations is replaced by (x – x0).

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