KINEMATICS AND DYNAMICS FOR HIGH SCHOOL
Average Speed
A scalar quantity is any quantity that has magnitude and no direction. Speed is a
scalar quantity. The average speed of something is defined by the formula:
Average speed 
Dis tan ce
Time
Example:
A train departs at 10.00 a.m. and arrives at another station at 11.00 a.m. Find the
average speed of the train if the distance travelled by the train 90km.
90 km
1hour
 90km / h
The answer is 90km/h.
Uniform speed
If a graph is used to represent the motion of a train is linear, then the train travels at
uniform speed. Uniform speed may be defined as such that the train moves through
equal lengths of its path in equal times. The train travels at the same speed at all
times.
Distance
Time
Displacement
Displacement is a vector quantity because it has magnitude and direction.
Velocity is defined by the formula:
Displacement
Time
Uniform velocity is when something moves in a fixed direction with uniform speed.
Both the magnitude and velocity are uniform. If something moves in a circle, the
velocity is not uniform even if the speed may be uniform.
Velocity=
Example:
If mom walks out of the house to the market and then back to her house, what is the
displacement of mom?
The answer is zero because her displacement is the shortest length between the
beginning point and the final point of destination. In this case, her final point and
beginning point are the same, which is the house. Therefore, the displacement is
zero.
Acceleration
If the velocity is not uniform, the velocity changes. The rate at which the velocity is
changing is called acceleration. It is the rate of change of velocity. This means that
the velocity is not constant.
V1V 2
a, Acceleration=
T1  T 2
V1=Final Velocity
V2=Initial Velocity
T1=Final Time
T2=Initial Time
For example, if a train slows down, it is decelerating or it has negative acceleration.
If a car moves in a circle, it is accelerating towards the centre of the circle.
Example:
A train increases its velocity from 3m/s at t=7s to 9m/s at t=10s. Find the
acceleration of the train.
6m / s
 2m / s 2
Acceleration=
3s
Uniform acceleration
The velocity of something is given by
v  u  at
a= uniform acceleration
t=time
u= initial velocity
If s is the distance or displacement travelled by something, then,
s=average velocity×t
If the acceleration is uniform, the velocity increases at a constant rate. The average
1
velocity in the time interval will equal to the velocity at the instant t that is the
2
mean of the velocities at the beginning and end of the time interval. Most of the
time, the velocity was less than at .
s  vavet 
1 2
at
2
1
(u  v)t
2
1
s  (u  u  at )t
2
1
s  ut  at 2
2
s
Also,
1
(u  v)t
2
1
(v  u )
s  (u  v)
2
a
2
2
1 (v  u )
s
2
a
2
2
v  u  2as
s
Dynamics
Dynamics explains how an object moves in terms of the forces which change its
motion.
A force is any cause which produces or tends to produce a change in the existing
state of rest of a body, or of its uniform motion in a straight line.
A force is a vector quantity.
According to Newton’s Laws of Motion
1. Every body continues in a state of rest or of uniform motion in a straight line
unless acted upon by external forces.
2. Change of momentum per unit time is proportional to the impressed force and
takes place in the direction of the straight line in which the force acts.
3. To every action there is always an equal and opposite reaction.
Newton’s first law of motion explains why a bowling ball continues rolling unless it is
stopped by the pins.
Newton’s second law of motion defines the equation:
Force  mass  accelerati on
Newton’s third law of motion explains why a cup which has weight, placed on the
table experiences a normal reaction force by the bottom of the table.
Normal
reaction
force
Weight
of cup