Mechanics is the branch of physics which deals with the cause and effects of motion of a particle, rigid
objects and deformable bodies etc. Mechanics is classified under two streams namely Statics and
Dynamics. Dynamics is further divided into Kinematics and Kinetics.
Motion is a combined property of the object and the observer. There is no meaning
of rest or motion without the observer. Nothing is in absolute rest or in absolute
motion.
Rectilinear motion is motion, along a straight line or in one dimension. It deals with the kinematics of a
particle in one dimension.
The average velocity of a moving particle over a certain time interval is defined as the displacement
divided by the lapsed time.
The velocity at a particular instant of time is known as instantaneous velocity.
The term “velocity†usually means instantaneous velocity
Average speed is defined as the total path length travelled divided by the total
time interval during which the motion has taken place. It helps in describing
the motion along the actual path
The average acceleration for a finite time interval is defined as :
Average acceleration =
time interval
change in velocity
Average acceleration is a vector quantity whose direction is same as that of the change in velocity.
The instantaneous acceleration of a particle is its acceleration at a particular instant of time. It is
defined as the derivative (rate of change) of velocity with respect to time. We usually mean
instantaneous acceleration when we say “ accelerationâ€. For straight motion we define instantaneous
acceleration as :
This expression suggests that the average velocity is equal to
the slope of the line (chord) joining the points corresponding to
· x- t graph is a straight line of slope u through xi.
· as velocity is constant, v - t graph is a horizontal line.
· a-t graph coincides with time axis because a = 0 at all time instants.
If a particle is accelerated with constant acceleration in an interval of time, then the motion is termed as
uniformly accelerated motion in that interval of time
In straight line motion, all the vectors (position, displacement, velocity & acceleration) will have only one
component (along the line of motion) and there will be only two possible directions for each vector
Slope - intercept form : y = mx + c is the equation of a straight line whose slope is m & which makes
an intercept c on the y-axis.
PARABOLIC CURVE-EQUATION, GRAPH (VARIOUS SITUATIONS UP, DOWN, LEFT, RIGHT
WITH CONDITIONS)
· x is a quadratic polynomial in terms of t. Hence x - t graph is a parabola
( i) Zero Velocity
As position of particle is fixed at all the time,
so the body is at rest.
Velocity vs time graph
Acceleration vs time graph
DISPLACEMENT FROM v - t GRAPH & CHANGE IN VELOCITY FROM a -t GRAPH
Area under v-t graph gives displacement, if areas below the t-axis are taken
negative.
MOTION WITH NON-UNIFORM ACCELERATION
(USE OF DEFINITE INTEGRALS)
This is another important expression for acceleration.
If a is in terms of x,
