Class 11 Motion in a straight line Study material in pdf

Motion in a Straight Line Class 11 Physics
As students embark on the journey into the fascinating realm of physics in Class 11, one of the fundamental topics that captivates their attention is "Motion in a Straight Line." This foundational concept forms the bedrock of kinematics, the branch of physics concerned with the description of motion. In this chapter, students explore the dynamics of objects moving along a linear path, unraveling the principles that govern their displacement, velocity, and acceleration. From understanding the basic distinctions between scalar and vector quantities to delving into the equations that quantify motion, Class 11 students embark on a captivating exploration of the fundamental laws that underpin the linear journey of objects in motion. Motion in a straight line not only serves as a gateway to more intricate concepts in physics but also provides a lens through which students perceive and analyze the dynamics of the world around them.
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1. TOPIC : motion in a straight line
CLASS : XI
SUBJECT : PHYSICS

2. To locate the position of object we require a
reference point (origin) and a set of axes.
Describing motion
The coordinates (x,y,z) describe the position of
object.
The coordinate system along with the clock is
known as the frame of reference.

3. The actual path length travelled by the object is
known as distance.
Distance:
It is Scalar quantity.
Displacement:
The change in position is known as displacement.
Displacement = Final position –Initial position
Δx = x
2–x
1
x
2> x
1,Δx–is positive
x
2< x
1,Δx–is negative

4. The motion of the object can be represented by
position –time graph.
Position – time Graph:(x-t graph)
t (S)
x (m)
0
1020 3040
10
20
30
40
t (S)
X (m)
0
12 3 4
2
4
6
8
Object is at restObject in uniform motion

5. Time (S)
Position(m)
0
1 2 3 4
2
4
6
8
Object in non-uniform motion
i.e. accelerated motion

6. Average velocity is defined as displacement (Δx)
divided by time interval (Δt)
Average velocity:
It is measured in ms
-1

7. Average Speed:
Average speed is defined as the total path
length travelled by the object divided by time
interval.
It is measured in ms
-1

8. t (S)
X (m)
0
Q
A
B
P
X-t graph for two children A and
B returning from their school O
to their houses P and Q resp.
Choose the correct entries in the
bracket
1.(A/B) lives closer to the school than(B/A)
2.(A/B) stars from the school earlier than(B/A)
3.(A/B) walks faster than(B/A)
4. A and B reach home at the (same/different) time.
5.(A/B) overtakes(B/A) on the road (once/twice)

9. Instantaneous Velocity:
The velocity at an instant is defined as the limit of
average velocity as the time interval becomes
infinitesimally small(Δttends to zero)
The instantaneous velocity is
also defined as the rate of
change of position at that
instant.
The instantaneous velocity is
the time derivative of
position.

10. Instantaneous Speed:
The magnitude of an instantaneous velocity is called as
instantaneous speed.
Speed associated with both the velocities will 25 ms
-1

11. Average acceleration is defined as change in velocity
(Δv) divided by time interval (Δt)
Average Acceleration:
It is measured in ms
-2

12. Instantaneous acceleration:
The acceleration at an instant is defined as the limit of
average acceleration as the time interval becomes
infinitesimally small (Δt tends to zero)
The instantaneous
acceleration is also defined
as the rate of change of
velocity at that instant.
The instantaneous acceleration is the time derivative of velocity.

13. x
x
t
t
x
t
O
O O
The Position –time graph
Positive
Acceleration
Zero
Acceleration
Negative
Acceleration

14. t
O
The velocity time graph
Object is moving in
positive direction
with positive
acceleration
v
0
v
t
O
v
0
v
Object is moving in
positive direction
with negative
acceleration

15. t
O
Object is moving in
negative direction with
negative acceleration
-v
0
-v
Object is moving with negative acceleration
through out. Between 0 to
t
1it moves + x-directionand
between t
1to t
2it moves in
opposite direction.
t
2
O
v
0
-v
t
1

16. Time (h)
Velocity(km)/h
0
1 2 3 4
10
20
30
40
o
B
c
AArea under Velocity-time Graph.
Velocity -Time Graph for object
moving with constant velocity.
Area under
graph
=
Area of
Rectangle
OABC
v
t
=OA x OC
= v x t
Product of velocity and time is equal to
displacement.
Areaunder Velocity –Time graph is always equal
to the distancetravelled by an object.

17. t0
E B
C
t
v-v
0
v
0
v
D
A
Kinematic equations of
uniformly accelerated motion
If the object is moving with constant
acceleration then inst,acceleration is
equal to av.acceleration
This is velocity-time relation
1.velocity-time relation
v = v
0+at

18. t0
E B
C
t
v-v
0
v
0
v
D
A
2. Position -time relation
Area under v-t graph.
A = Ar.ofRec.OACD +Ar of Tri. ACB
A = (AO x OD)+ ½ (Ac x BC)
A = (v
0x t)+ ½ (v-v
0) x t
A = v
0t + ½ (v
0+at-v
0) x t
A = v
0t + ½ a t
2
x = v
0t + ½ a t
2
x –x
0= v
0t + ½ a t
2

19. t0
E B
C
t
v-v
0
v
0
v
D
A
3.Position –velocity relation
Area under v-t graph.
Area of trapezium OABD
A = ½ x OD (OA +BD)
A = ½ x t (v
0+v)
A = ½ x (v-v
0)/a x (v
0+v)
A = (v-v
0)x (v + v
0)/2a
A = (v
2
-v
0
2
)/2a
x = (v
2
-v
0
2
)/2a
x-x
0= (v
2
-v
0
2
)/2a
2a(x-x
0)= v
2
-v
0
2

20. Home work
•1.A ball thrown vertically upwards with a
speed of 19.6 m/s from the top of the tower
returns to the earth in 6 seconds. Find the
height of the tower.
•2.A car moving along the straight highway
with a speed of 126 km/h ,is brought to a
stop within a distance of 200 m. What is the
retardation of the car and how long does it
take for the car to stop?

21. Equations of motion by Calculus method
1. velocity-time relation.
Acceleration
Integrating on both sides
This is velocity-time
relation.

22. velocity
2. Position-time relation.
Integrating on both sides
This is Position-time
relation.

23. 3.Velocity-Position relation.
Integrating on both sides
This is velocity-
Position relation.

24. Consider two objects A and B moving
uniformly with average velocities v
A and v
B along x-axis. If
x
A (0) and x
B (0) are positions of objects A and
B,respectively at time t = 0, their positions x
A(t) and x
B(t)
at time t are given by:
x
A(t ) = x
A (0) + v
At --------1
x
B(t) = x
B(0) + v
Bt --------2
displacement of object B w.r.t. object A is
x
BA(t) = x
B(t) –x
A(t)
x
BA(t) = [ x
B(0) –x
A(0) ] + (v
B–v
A) t. ----3
Object B has a velocity v
B–v
A w.r.t. A
Relative velocity

25. The velocity of object B relative to object
A is v
B –v
A
v
BA= v
B –v
A
The velocity of object A relative to object
B is v
A –v
B
v
AB= v
A –v
B

26. O
20
40
60
80
100
120
140
X(m)
t(s)
O
20
40
60
80
100
120
140
t(s)
X(m)
123456
123456
A
B
A
B
v
A= v
Bv
A–v
B = 0v
B -v
A= 0
The two objects stay
at a constant distance
v
A> v
B
v
B -v
Ais negative
Objects meet at a
common point

27. O
20
40
60
80
100
120
140
t(s)
X(m)
123456
A
B
v
A and v
Bare of opposite signs.
In this case, the magnitude of v
BA or v
ABis
greater than the magnitude of velocity of A or
that of B