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