Uniformly Acceleration Motion

Position

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 

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Velocity

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

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Acceleration

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

]

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