Plane Curvilinear Motion: x-y Coordinates

 

Solving plane curvilinear problems

 

Almost every particle curvilinear kinematic problem can be solved by manipulating the following three equations.

 

• Velocity: v = dr/dt
• Acceleration: a = dv/dt
• Acceleration as a function of position: a dr = v dv

 

If the velocity or acceleration are dependent of time, the above velocity and acceleration equations may be integrated to find position or velocity.

 

• Velocity → Position: v = dr/dt   →   ∫v dt = ∫dr
• Acceleration → Velocity: a = dv/dt   →   ∫a dt = ∫dv