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The speed of a body is determined by the amount of distance it
travelled in a given time interval in any direction, therefore speed is
scalar quantity (quantity without direction). For example, the train
passed 200 km in 2 hours, so the speed of train is equal to 100 km per

hour, but we know nothing about the direction of motion. If the same
train passed 200 km in the north direction, therefore vector of
displacement is known then displacement in a given time interval is

vector value named velocity. And now consider much more
explanatory characteristics of motion of material point or body in
translatory motion /
If in any equal intervals of time, no matter how small they are, the

body passes equal sections of distance, such motion is called uniform. In
such motion, the ratio of the distance to the time, in which this distance
was passed, is the constant value. Such ratio is called the speed of the

uniform motion .
Speed of a material point is the quotient by dividing distance S
traveled by the time taken:

S
v 
t . (1.5)
Like distance traveled, speed is a scalar quantity. Speed and
magnitude of a velocity vector are expressed in meters per second (m/s).

From (1.5) follows distance-time equation
S  v t  (1.6)
or

S  S  vt
0 (1.7)
where S is the distance with origin of reference at time moment t = 0.
0
If at any equal intervals of time, no matter how small they are, the
body passes different sections of distance such motion is called non-
uniform and in this case the ratio of the distance to the time, in which

this distance was passed, is average speed.
 S
 v 
t  . (1.8)
Only in limit, when interval of time approaches ∆t→0 we can consider

non uniform motion as uniform one. Therefore
 S dS /
v lim   S
 t 0 t dt . (1.9)
It means instantaneous speed is the first derivative of distance with
respect to time.

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