Kinematics deals with objects in motion without going into the details
of the causes of motion.
In this we find the basic terms of physics like the distance,
displacement , speed, velocity , time , acceleration etc.
Distance is the change in position of an object. It is how far an object
travels or how far away something is located.
Example: if your school is 10 km from your home then the distance
between your home and school is 10km and vice versa.
Metric Units of measurement of distance: mm, cm, m , km, light years
Common English units: feet,inch.
SI units: meters.
Time: time is measured in seconds , minutes or hours.
Seconds is the smallest unit. 1 second =1/60 minutes
And 1 second= 1/3600 hours
That is , 3600 seconds make an hour and 60 seconds make a minute
1 minute=60 seconds =1/60 hours
Example: 2 hours= 2 x 60 minutes=120 minutes
2 hours= 2 x 60 x 60 = 7200 seconds.
15 minutes=15/60=1/4 th hour
15 minutes= 15 x 60 =900 seconds.
Speed: It is the distance travelled in a given time .
Speed = distance / time .
Units of speed : km/h or m/s or cm/s ft/s etc
Observe that the speed units have both distance and time units
Example: if you drive 100 km in a couple of hours the speed of your
car is
Speed =distance/ time = 100 km / 2 hours = 50 km / h
The basic definitions defined here are important when objects travel
at a constant speed.
Average speed : It is defined as the total distance covered in a given
total time.
If speed changes with time then the object is said to have variable
speed or the object is said to be accelerating.
2. Lisa rides her car at a top speed of 50m/s in 10 s. What distance
did she travel in these 10 s.
Solution: rearrange the distance time formula .
=50 x 10 = 500 m.
3. Jerry runs 60 m at a speed of 4 m/s. Find the time taken by Jerry
to cover the 60m distance.
Solution : we can use the same distance , time , speed formula to get
time
It is the shortest distance between two distinct points or locations .
Here an important thing to observe is the direction of travel.
For example Going 100 m from home to school is towards east, we
take it as +100 m.
The same 100m when it is travelled from school to home is towards
west and so – 100 m.
Here total displacement in going from home to school and then from
school to home is 100 + (-100)=100-100 = 0 .
But actual distance travelled is 100 +100 =200 m .
This is how we consider the term displacement.
Example: one more example may clarify this further.
Suppose you travel from your school to a friends’s place which is 50
m away and then return to your home , total displacement is (100 +
50 ) -100 = 50 m
The physical quantity which gives the ratio of displacement and time
is called velocity.
Velocity is the rate of change of displacement.
If starting position is xi and final position is xf then the total
displacement is xf - xi and time taken is tf - ti .
Then velocity = displacement / time = (xf - xi) /( tf - ti )
Units of velocity are similar to speed units.
Average velocity is defined as the ratio of total displacement to
the total time taken.
Average velocity = (d1+d2+----+dn) / (t1+t2+t3+----+tn)
If vi and vf are the initial and final velocities , then
Vavg = (vi+vf)/2
Acceleration:
Whenever velocity increases or decreases there will be
acceleration .
Acceleration is defined as the rate of change of velocity.
Units : It has the units of velocity and time ,like m/s/s or m/s2 or
km/h2 and so on.
a= ( vf - vi ) / (tf - ti )
example: a car moving at 50m/s increases its velocity to 100 m/s
in 10 seconds. Then it is said to accelerate and the acceleration
is given as
a= (100 -50)/(10-0) = 50/10=5 m/s2
suppose the car slows down from 100 m/s to 50 m/s in 10 s then
a= (50- 100)/(10-0) = -5 m/s2
in this case the car is said to be decelerating . Deceleration is
negative acceleration.
Important note: Displacement, velocity and acceleration all have
directions.
Another way to describe them is all these three are vectors.
Example: A train running at 80 km/h increases its velocity to 120
km/h in 3 hours. What is the acceleration of the train.
Solution : a = change in velocity / time
a = (120 – 80) / (3-0) = 40 / 3 =13.3 km/h2
Equations of motion
Any problem involving motion can be solved using the equations of
motion.
1. Simplest equation is derived from the basic definition of
acceleration.
a = (vf – vi)/t
re arranging the terms, a t = vf - vi
or vf = vi + at
2. Average velocity is defined as vavg = (vf + vi )/2 ------(1)
Displacement = d = (vavg) t ----------- (2)
Plug in v avg from the equ (1) into equ 2
And t = (vf-vi)/a from the definition of acceleration.
Then d = [(vf + vi )/2 ][ (vf-vi)/a ]
d = (vf+vi)(vf-vi)/2a
 d = vf 2 – vi 2 /2a
 vf 2 = vi 2 + 2ad
This equation is used whenever an object travels with a constant
acceleration and there is no involvement of time.
3. Consider an object that has an initial velocity vi and is traveling
with a constant acceleration a. After a time t let d be the
displacement .
d = [(vf+vi )/2 ] t = [(vi+at )+vi]/2 x t = vi t + ½ a t2