Average Velocity

Vave = ∆d/∆t

Vave = d2-d1/t2 - t1

The average velocity equals the change in position divided by the change in time.  Average velocity is the slope of a position vs time graph.

Distance traveled with an average velocity.

∆d = (Vave)(∆t)

Distance equals average velocity multiplied by change in time. 

Instantaneous Velocity

V(t)

Slope of the tangent for a single point on a position-time curve.

Instantaneous Velocity

V(t) = lim    ∆s = ds

        ∆t->0  ∆t     dt  

s = displacement. Velocity is the first derivative of displacement.

Average Acceleration

aave = ∆V/∆t

aave = V2 - V1/t2 - t1

Average acceleration equals the change in velocity divided by the change in time.  Average acceleration equals the slope of a velocity time graph.

Instantaneous Acceleration

a(t)

Slope of the tangent for a single point on a velocity-time curve.

Instantaneous Acceleration

a(t) = lim   ∆v = dv =d2s

       ∆t->0  ∆t     dt    dt2

s = displacement. Acceleration is the first derivative of velocity and the second derivative of displacement. 

Final velocity after uniform acceleration

Vf = Vi + at

Final velocity as related to initial velocity, acceleration and time.

Displacement when initial velocity, final velocity and time are known

d = 1/2(Vf + Vi)t

Displacement as related to initial velocity, final velocity, and time.

Displacement when initial velocity, acceleration and time are known

d = Vit + 1/2at2

Displacement as related to initial velocity, acceleration and time.

Final velocity when initial velocity, acceleration and displacement are know.

Vf2 = Vi2 + 2ad

Acceleration as related to initial velocity, final velocity, and time

Position vs. time graph

V

The slope of the graph gives the velocity

Velocity vs. time graph

a and d

The slope of the graph gives the acceleration.  The (signed) area between the graph and the time axis gives the displacement.

Acceleration vs. time graph

∆V

The (signed) area between the graph and the time axis gives the change in velocity.

Slope of a curve

Rise/Run

The ratio of vertical separation of two points on a curve (rise) to the horizontal separation of the points (run) is the slope of the curve.