Mechanics

# Uniformly Varied Movement

Uniformly varied rectilinear motion occurs when an object undergoes constant changes in velocity, which causes an increase or decrease in this magnitude.

In Physics , we define a uniformly varied motion as one that has a constant, non-zero scalar acceleration . In this type of motion, the average scalar acceleration is also constant and equal to the instantaneous one.

a (constant ≠0)

to m   (constant ≠0

a = Δ v or even Δ v = a. Δ t
Δ t

Regarding the equation of motion uniformly varied above, we can mention two properties:

• The change in speed is directly proportional to the time interval Δt.
• For equal time intervals, we will have equal changes in speed.

Hourly equation of speed in the MUV

Where 0 is the initial speed corresponding to 0 = 0, and where v is the speed at a generic instant t , we have:

Δ v = v- v 0
Δ t = t- t 0 → Δ t = t – 0

Being:

Δv = a. Δt

Therefore:

(v- v 0 ) = a.(t-0)
vv 0 = at
v = v 0 + at

The above expression is called the hourly equation of the velocity of uniformly varied motion. Note that 0 and a are constants and that velocity v and time t are two variables. The equation demonstrates, then, that the law relating v to t is of the 1st degree in t .

By graphically representing this velocity as a function of time, we will obtain a straight line oblique to the axes . Another interpretation of this equation can be seen in the graph below. For instant t , it is clear which parts correspond to 0 and the product a. t .

Space time equation

Let’s look at the figure above. The yellow area under the vxt graph represents the space variation Δs. Therefore, we can say that the value of the variation of space is equal to the area of ​​the trapezoid . To calculate this area, we must divide the trapezoid into two figures: a triangle and a rectangle.

Δ = bh = (t-0).v 0 = v 0 .t

Δ bh = (t-0).at = at 2
2 2 2

Δs = v 0 .t + at 2
2

or breaking up Δs = (s – s0), we have:

s – s 0 = v 0 .t + at 2
2

s = s 0 + v 0 .t + at 2
2

This equation shows how space, or abscissa, s varies with time. Hence, it is called the time equation of space . Note that s is a 2nd degree function on t .