Motion in a Plane

Position

Position, displacement, velocity, and acceleration are expressed as vectors even for straight-line motion. Displacement s = x₂ - x₁, velocity v = ds/d

Any motion in a plane can

Any motion in a plane can be resolved into two independent motions along perpendicular axes (x and y). Position vector r = xî + yĵ, velocity v = (dx/d

Relative velocity of object A

Relative velocity of object A with respect to B is v̲ₐᵦ = v̲ₐ - v̲ᵦ. This vector subtraction gives both magnitude and direction of relative motion. Ap

Motion of objects under gravity's influence

Motion of objects under gravity's influence with initial velocity at angle θ. Horizontal motion: vₓ = u cos θ (constant), x = (u cos θ)t. Vertical mot

Motion in a circle with constant

Motion in a circle with constant speed v. Angular speed ω = v/r = 2π/T where T is period. Centripetal acceleration aᶜ = v²/r = ω²r directed toward cen