The document discusses motion in one dimension. It defines motion, rest, and different types of motion such as translational, rotational, and vibrational. It focuses on one-dimensional motion along a straight line. Key terms discussed include displacement, distance, average speed, average velocity, uniform and non-uniform motion, acceleration, and kinematic equations. Graphs of displacement-time, velocity-time and acceleration-time are presented. Motion under gravity and upward vertical motion are also summarized using kinematic equations.

1. By
SANJEET SINGH

2. Motion in 1-D/ Motion in a straight line
Mechanics is a branch of physics which deals with the study of motion of a particle. Motion is
change in position of the object with respect to time. Different kinds of motion are translational,
vibrational and rotational. In translational motion, a particle moves from one point to another
point along a straight line. In rotational motion particles of the body describes concentric circles
about axis of rotation. In vibrational motion particle performs to and fro motion about mean
position. In this chapter we shall confine ourselves to the study of motion of objects along a
straight line, also called as rectilinear motion.
Motion: If an object changes its position w.r.t. its surroundings with time, then it is called in
motion.
Rest: If an object does not changes its position w.r.t. its surrounding with time, then it is called at
rest.
[Note: Rest and motion are relative states. It means an object which is at rest in one frame of
reference can be in motion in another frame of reference at the same time.]
Point Mass Object: An object can be considered as a point mass object, if the distance travelled
by it in motion is very large in comparison to its dimensions.
Types of Motion:
(1) One Dimensional Motion: If only one out of the three coordinates specifying the position of
the object changes with respect to time, then the motion is called 1-D motion e.g. motion of a
train along a straight line, an object falling under gravity etc.
(2) Two Dimensional Motion: If only two out of three coordinates specifying the position of the
object changes with respect to time, then the motion is called 2-D motion e.g. A circular motion.
(3) Three Dimensional Motion: If all the three coordinates specifying the position of the object
changes with respect to time, then the motion is called 3-D motion e.g. a flying bird, a flying
aero plane, random motion of gas molecules etc.
Path length (or Distance):
It is the actual distance travelled by the body during its motion. It is a scalar quantity.
Displacement:
The shortest distance between the initial and final position of a body during its motion is
called its displacement. It is a vector quantity.

3. Distance or total path length covered= (4 km+ 3 km) = 7 km
Displacement = 2 2
4 3 25 5 km   2
[Note: (a) distance displacement
(b) The path length (or distance) and displacement are equal only if the object doesn’t
change its direction during its motion. In all the other cases the path length is greater than the
magnitude of the displacement.]
Average Speed:
Average speed of a particle is defined as the total path length travelled divided by total
time interval during which the motion has taken place.
Total path length
Average speed=
Total time interval
[Note: (a) Speed is a scalar quantity.
(b) The speed of a particle can be zero or positive but never negative.]
Average Velocity:
Average velocity is defined as the change in displacement divided by the time interval in
which the displacement occurs.
Displacement
Average velocity=
Time interval
[Note: (a) Velocity is a vector quantity.
(b) The average velocity of a particle can be zero, positive or negative.]
Question: The average speed of an object is greater than or equal to magnitude of average velocity over
a given time interval. Explain.

4. Problem: A car moves at a constant speed of 60 km/hr for 1 km and 40 km/hr for next 1 km.
What is the average speed of the car?
Solution:
1 2 1 2
1 21 2
1 2
total distance travelled
Average speed=
total time taken
1 1 2 2 120
48 km/hr
1 1 5 5
60 40 120
x x x x
x xt t
v v
   
     
 
Instantaneous speed and Instantaneous velocity:
It is the rate of change of position with respect to time at a particular instant.
Or,
When an object is travelling with variable speed, then its speed at a given instant of time is called
its instantaneous speed.
dx
v
dt

[Note: The speedometer of an automobile measures the instantaneous speed of the automobile]
Uniform motion:
The motion of a body is said to be uniform if it covers equal distances in equal interval of time.
Non-uniform or Variable Speed:
If an object covers unequal distance in equal intervals of time, then its speed is called non-
uniform or variable speed.
Acceleration: The rate of change of velocity with respect to time is called acceleration.
Change in velocity
Acceleration=
time
[Note: Acceleration can be positive, zero or negative. Positive acceleration means velocity
increasing with time, zero acceleration means velocity is uniform while negative acceleration
(retardation) means velocity decreasing with time]

5. Graphs:
(1) Displacement time graph ( x t graph):
[Note: Slope of displacement-time graph gives average velocity]

6. (2) Velocity time graph (v t graph):
[Note: Slope of velocity- time graph gives average acceleration]

7. (3) Acceleration time graph ( a t graph):
Kinematical Equations (for uniformly accelerated motion):
(i) v u at 
  
(ii) 21
2
S ut at  (iii) 2 2
2v u aS 

Motion under gravity:
For an object falling freely under gravity, equation of motion takes the form
(i) v u gt  (ii) 21
2
h ut gt  (iii) 2 2
2v u gh 
[Note: If an object is thrown upward then, g is replaced by g in above equations]
Upward Vertical Motion:
(i) v u gt  (ii) 21
2
h ut gt  (iii) 2 2
2v u gh 

8. [Note: (a) Time taken to reach maximum height (at max. height, 0v  )
2
A
hut
g g
 
(b) Maximum height reached by the body,
2
max.
2
u
h
g

(c) A ball is dropped from a building of height h and it reaches after t seconds on earth. From
the same building if two balls are thrown (one upwards and other downwards) with the same
velocity u and they reach the earth surface after 1t and 2t seconds respectively, then 1 2t t t .
(d) When a body is dropped freely from the top of the tower and another body is projected
horizontally from the same point, both will reach the ground at the same time.]