# Uniformly Accelerated Motion

### Uniformly Accelerated Motion

Uniformly Accelerated Motion - Animation Learnchannel

As 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 ⋅ t2     ... Eq. (2)

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

s =    v2          ... Eq. (3)
2 a

#### Forces on the inclined plane

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

Forces on object sliding downhill - decomposing weight force

• the normal force FN which is the force that always acts perpendicular to the surface on which the object is resting.
• the downhill force FD, which is actually the force that accelerates the body.

The weight force is calculated as:

FG = m * g | Mass m in kg and gravity g = 9,81 m/s2

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

• FD = FG  cos α
• FN = FG  sin α