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The Equations of Motion
These equations are useful for solving problems in which objects are moving with uniform acceleration.  
If the sense of the motion changes, decide which sense is positive before starting the calculations  
Definitions  
Quantity Definition Vector/Scalar S.I. unit
 Displacement  distance moved in a specified direction* v m
 Speed  distance moved per unit time s ms-1
 Velocity  distance moved per unit time in a specified direction v ms-1
 Acceleration  change in velocity per unit time v ms-2
 
 
*Alternatively: distance from a fixed reference point, measured in a specified direction.  
In the following equations:  
t   represents time
a   represents acceleration
u   represents initial speed (or initial velocity)
v   represents final speed (or final velocity)
s   represents the displacement from some reference point (usually the starting point) at time t
If the reference point is not the starting point, we will also see so in the equations (where so means the displacement at t = 0)
 
 
The equations will give us the magnitude and sense of the velocities, accelerations and displacements  
   
Velocity/Time Graph for the type of Motion considered
     
1. Average velocity, va is given by
   
     
2. Therefore we have
   
     
3. The definition of acceleration gives
   
4. Equation 3 is often rearranged to give  
     
5. Combining equations 2 and 4 in order to eliminate v gives
   
 
6. Combining equations 3 and 5 in order to eliminate t gives
 
 
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