PCM
KINEMATICS-1
say wow, not how.
WHAT IS KINEMATICS?
Kinematics is the study of motion without analyzing its' cause.
In physics, motion is a change in position of an object over time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, time, and speed.
TYpes of motion
-
One Dimentional Motion
Motion along ANY straight line from one line to another.
-
Two Dimentional or Planar Motion
Any sort of motion on a plane. eg) circular motion
-
Three Dimentional Motion
Any motion other than along a plane or straight line is called 3-D Motion.
Motion in one dimention
Notes:
-
The line of motionwill be considered X-axis in general.
-
the point from where the motion starts can be treated as origin in general.
-
the direction of the vector quantities is given by + and - signs itself.
-
use of i,j or k cap signs are not required.
Quantities:
POSITION:
The X Co-ordinate of the particle with respect to the origin represent origin of a particle.
DISPLACEMENT:
Change in position. S= X
DISTANCE:
The path travelled by the body is known as the distance.
| Displacement| >/= Distance if the particle doesnt turn.
VELOCITY:
The rate of change of position with respect to time.
V= dx/dt
AVG. VEL:
The rate of change of position with respect to time.
V= s/t
V1+V2 is NOT Average Velocity!! It only holds when accn is constant 2
SPEED:
The magnitude of instantaneous velocity.
V= | ds/dt |
Speed can also be called d(rate of distance)/dt
|Avg Vel| </= Avg Speed when displacement and distance are equals, i.e particle doesnt turn.
Vertical motion under gravity
Notes:
-
Gravity will ALWAYS be taken negative, EVEN in the downward direction.
-
Upward and downward motion is always symetrical.
Symettry:
-
At any two symetrical points, one can find the same velocity.
-
at maximum height, v=0
IMPORTANT:
If a particle is thrown vertically upwards, at initial velocity u, find:
1) TIME of ascent& descent
v=0
u
a= -g
v= u+at
0= u+ (-g)t
-u= -gt
u = t g
2) TOTAL HEIGHT
u
v=0
h= ut+ at /2
h= u^2/g+ u/2g
h= (2u^2+u)/2g
h=u(2u+1)/2g
2
3) TIME OF FLIGHT
2t
= 2u/g
u
v=0
Snth= u+a(2n-1)/2
the distance between n and (n-1) seconds.
PROJECTILE MOTION.
IMPORTANT FORMULAE.
T=2usin@ =2Uy
g g
[only ground to ground]
R=usin2@ = 2UxUy
g g
2
[everywhere]
H=usin@ = 2Uy
2g 2g
[everywhere]
2
2
2
If particle is projected at same speed at complimentary angles then Range remains same.
IF MAX HEIGHTS ARE H1, H2 then
H1=usin@
2g
H2=ucos@
2g
2
2
2
2
H1 = tan@
h2
2
r=4 h1h2
