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 s_{o} in the equations (where s_{o}
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, v_{a} 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 





