• Mechanics
• /
• Kinematics
• /
• Basic motions

## Uniform Motion

It is a movement in which the scalar speed is constant and different from zero $$v(t) = v_0 = \mbox{constant} \ne 0$$. The position as a fuction of time, for this movement, is: $$s(t) = s_0 + v_0 t.$$

The figure below illustrates the graph $$s \times t$$ of this movement, which, in this case, is always a straight line, that increases with time if $$v_0 \gt 0$$ and decreases with time if $$v_0 \lt 0$$. Graph $$s \times t$$ to $$v=constant\gt0$$. In the uniform motion, where the speed is positive and does not change, the graphic of the position versus time is a straight line (red line). The slope of this straight line (blue slope) is related to the speed, greater speed means greater slope.

## Uniformly accelerated motion

Uniformly varying motion is the movement in which scalar acceleration is constant and nonzero, $$a(t)=\mbox{constant} \ne 0$$.

The functions for this type of movement are:

The position as a fuction of time
$$s(t) = s_0 + v_0 t + a \frac{t^2}{2}.$$
The speed as a fuction of time
$$v(t) = v_0 + a t.$$
The Torricelli's equation
$$v^2 = v_0^2 + 2 a \Delta s,$$ and, in this case, $$v$$ is related to $$\Delta s$$.
In all these cases, $$a$$, $$s_0$$ and $$v_0$$ are constant, i.e., does not change in the time interval of interest, different from $$s(t)$$ and $$v(t)$$ that are always changing.

### Graphics and interpretations

The graphics for this movement and their interpretations are presented below.

Space $$\times$$ time $$(a > 0)$$
Space $$\times$$ time $$(a < 0)$$
Speed $$\times$$ time $$(a > 0)$$ The area $$A$$ under the graphic curve $$v \times t$$, yellow region, is the distance traveled by the object from $$t_0$$ to $$t_1$$. In the same graph, the acceleration is given by the slope of the line, therefore, if the acceleration was negative, the graph would be a straight line inclined downwards. # STUDY PHYSICS ANYTIME ANYWHERE Dynamic Exams Differentiated Content Top approval rate