### Uniformly Accelerated Motion

Table of Contents

ToggleAs you can see from the experiment above, the velocity v of the ball increases constantly. The acceleration a corresponds to the gradient of the v(t) diagram:

The distance s traveled increases exponentially and can be calculated:

**s = ½ s ⋅ t ^{2}** ... Eq. (2)

Eq.(1) converted to t and then inserted into Eq. (2) shows a relationship between the variables s, v and a:

**s = v ^{2} ** ... Eq. (3)

**. 2 a**

#### Forces on the inclined plane

The weight (force of gravity F_{g} ) is not the force that accelerates the object. But we can determine the force which accelerates the object by decomposing the force:

- the
**normal force****F**which is the force that always acts perpendicular to the surface on which the object is resting._{N} - the
**downhill force F**, which is actually the force that accelerates the body._{D}

The weight force is calculated as:

**F _{G} = m * g** | Mass m in kg and gravity g = 9,81 m/s

^{2}

If the weight force is known, the remaining forces can be determined using the trigometry:

**F**_{D}= F_{G}cos α**F**_{N}= F_{G}sin α