Uniformly Accelerated Motion

Introduction

A movement with uniformly increasing or decreasing speed is called uniformly accelerated motion .

Experiment

A car accelerates on a straight path. At certain points travel time and traveled distance are measured and recorded.

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\( s \) in \( \rm m \)
\( t \) in \( \rm s \)
\( v \) in \( \rm \frac{m}{s} \)
\( a \) in \( \rm \frac{m}{s^2} \)

Results

The distance-time curve is a parabola.

$$ s = \dfrac{a}{2} \cdot t^2 $$

The velocity-time curve is a straight line passing through the origin. This shows that the speed and the time are proportional to each other.

The proportionality constant is obviously the acceleration \(a \) of the body.

$$ v = a \cdot t $$

The acceleration-time curve is a straight line extending parallel to the x axis. This shows that the acceleration remains the same over the whole trip. The following applies:

$$ a = \text{konst.} $$

Units of velocity

To specify the velocity the units \(\rm \frac{m}{s} \) and \(\rm \frac{km}{h} \) are often used. They can be converted into each other as follows:

$$ \rm 1 \,\, \dfrac{km}{h} = \dfrac{1000 \,\, m}{3600 \,\, s} = \dfrac{5}{18} \dfrac{m}{s} $$
$$ \rm 1 \,\, \dfrac{m}{s} = \dfrac{0,001 \,\, km}{\frac{1}{3600} \,\, h} = \dfrac{0,001 \cdot 3600}{1} \dfrac{km}{h} = 3,6 \,\, \dfrac{km}{h} $$

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