Quantity Value
Value in component form
DisplacementΔr ( Change in position ) r ’ - r îΔx + ĵΔy
Average Velocityv̅
( ratio of displacement and corresponding time interval )
Δr / Δt vxî + vy ĵ
vx = Δx / Δt , vy = Δy / Δt
Instantaneous velocityv
( limiting value of average velocity as the time interval approached zero ) dr / dt vxî + vy ĵ
vx = dx / dt , vy = dy / dt
Magnitude of v
Direction of v , θ
( direction of velocity at any point on the path is tangential to the path at that point and is in the direction of motion ) tan -1 ( vy / vx )
Average Accelerationa̅
( change in velocity divided by the time interval )
Δv / Δt ax î + ay ĵ
ax = Δvx / Δt , ay = Δvy / Δt
Instantaneous accelerationa
( limiting value of the average acceleration as dv / dt ax î + ay ĵ
ax = dvx / dt , ay = dvy / dt
ax = d 2 x / dt 2 , ay = d 2 y / dt 2