Kinematics and dynamics of a particle
Kinematics and dynamics of a particle
This domain examines particle motion using the constant-acceleration equations, calculus for variable acceleration, projectile motion, and Newton's second law in one or two dimensions. Questions often require a force diagram plus a motion calculation.
Core rules
- Use v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t only when acceleration is constant.
- For variable acceleration, a = dv/dt = v dv/dx; integrate and apply initial conditions.
- Newton's second law is vectorial: resultant force = ma. Resolve along and perpendicular to motion; include weight mg, normal reaction, tension and friction where present.
- In projectile motion horizontal acceleration is zero and vertical acceleration is −g; the components share the same time. Find time from vertical motion, then range from horizontal motion.
Worked example
A 2 kg particle on a smooth horizontal plane is pulled by a 10 N force at 30° above the horizontal. The horizontal component is 10 cos 30° = 8.66 N, so a = 8.66/2 = 4.33 m s⁻². From rest for 3 s, v = 0 + 4.33 × 3 = 13.0 m s⁻¹ and s = ½ × 4.33 × 3² = 19.5 m.
Common traps
Using SUVAT when acceleration varies; omitting the normal reaction or resolving the weight incorrectly; losing direction signs; treating projectile components as independent in time; and mixing metres with centimetres.