Position in the uniformly accelerated motion depends on the initial position of the object x0, initial velocity of the objectv0, and the acceleration of the object a. Acceleration is the ratio of total velocity change taken over time interval. The displacement-time graph in the uniformly accelerated motion consists of a curved-line whose gradient (slope) is increasing in time.
The position of an object during uniformly accelerated motion can be described as:

x(t)=x0+v0t+

at2

2

[m]
where:
x0 - initial position of the object
v0 - initial velocity of the object
a - acceleration of the object
t - time of the movement 

Velocity in the uniformly accelerated motion depends on the initial velocity of the object v0, and the acceleration of the object a. The velocity-time graph in the uniformly accelerated motion consists of a straight-line whose gradient (slope) is increasing in time.
The velocity of an object during uniformly accelerated motion can be described as:

v(t)=v0+/−at[

m

s

]
where:
v0 - initial velocity of the object
a - acceleration the object
t - time of the movement

Acceleration is defined as the rate of change of velocity with respect to time, in a given direction. The SI units of acceleration are m/s2. It means that if an object has an acceleration of 1 m/s2it will increase its velocity (in a given direction) 1 m/s every second that it accelerates. The acceleration-time graph in the uniformly accelerated motion consists of a straight-line whose no gradient (slope) is increasing in time.
The average acceleration of an object during uniformly accelerated motion can be described as:

aśr(t)=

v(t)−v0

t−t0

[

m

s2

]
where:
v(t) - final velocity at moment t
v0 -initial velocity
t - time of the movement
t0 - initial time

The instantaneous acceleration can be found by differentiating position with respect to time twice or differentiating velocity with respect to time once:
a(t)=

dv

dt

=

d

dt

(

dx

dt

)=

d2x

dt2

[

m

s2

]

Linear motion is motion along a straight line. It can be described mathematically using only one spatial dimension. The motion of an object along a line can be described by its position x, which varies with time t.

There are two types of linear motion:
- uniform linear motion with constant velocity or zero acceleration
- non uniform linear motion with variable velocity or non-zero acceleration

Displacement is the shortest distance from the initial position x1 to the final position x2 of an object. Linear motion is a motion in a single dimension, the distance traveled by an object in particular direction is the same as displacement. The SI unit of displacement is the meter [m].
The displacement from the initial position to the final position of the object can be described as:

Δx=x2−x1[m]
where:
x1 - initial position of the object
x2 - final position of the object

Velocity is defined as the rate of change of displacement with respect to time. The SI unit of velocity is the meter per second ms[−1]. The average velocity is the ratio of total displacement Δx taken over time interval Δt.
The average velocity from the initial position to the final position of the object over time can be described as:
vav=

Δx

Δt

=

x2−x1

t2−t1

[

m

s

]
where:
x1 - initial position of the object
x2 - final position of the object
t1 - the time at which the object was at position x1
t2 - the time at which the object was at position x2

The instantaneous velocity is the measure of velocity of an object at a particular moment. Instantaneous velocity can be found by differentiating the displacement with respect to time.
The instantaneous velocity of an object with displacement in time can be described as:
vin=

lim

Δt→0

Δx

Δt

=

dx

dt

[

m

s

]
where:
Δx - displacement
Δt - time

Acceleration is the rate at which the velocity of an object changes with time. The SI unit of acceleration is the meter per square second m/s2. Acceleration is the ratio of total velocity change Δvtaken over time interval Δt.

a=

lim

Δt→0

Δv

Δt

=

dv

dt

[

m

s2

]
where:
Δv - velocity change
Δt - time change

The average acceleration is defined as the rate of change of velocity Δv with respect to time Δt:
aav=

Δv

Δt

=

v2−v1

t2−t1

[

m

s2

]
where:
t1 - the time at which the object had velocity v1
t2 - the time at which the object had velocity v2

The instantaneous acceleration can be found by differentiating position with respect to time twice or differentiating velocity with respect to time once:

a(t)=

dv

dt

=

d

dt

(

dx

dt

)=

d2x

dt2

[

m

s2

]