Kinematics Concepts (AP)

Kinematics Concept Algebraic Graphical

Calculus
Position, x      
Displacement, delta x
delta x = xsubf - xsubi

Area under v vs. t graph

delta_x = int(v(t) dt)
Time Interval, delta_t
delta_t = t_subf - t_subi
    
Average Velocity, v bar
v_bar = delta_x/delta_t
 Slope of secant line on x vs. t graph  
Instantaneous Velocity, v   Slope of tangent line on x vs. t graph
v definition
Change in Velocity, delta_v
delta_v = v_subf - v_subi
 Area under a vs. t graph
delta_v = int(a(tA) dt)
Average Acceleration, a_bar
a_bar = delta_v/delta_t
 Slope of secant line on v vs. t graph  
Instantaneous Acceleration, a   Slope of tangent line on v vs. t graph
a definition
Average Speed
   
Instantaneous Speed
magnitude of the instantaneous velocity
   
Equations for Constant Acceleration
v=vsub_o + at
v_bar = (v_sub_o + v)/2
delta_x = v_bar t
delta_x = v_sub_o t + (1/2) at^2
v^2=v_sub_o^2 +2a delta_x

last update September 30, 2008 by JL Stanbrough