Kinematics and Dynamics
What the exam tests
This domain tests motion graphs, uniformly accelerated motion, Newton's three laws, momentum and impulse, work-energy transfers, power, and collisions. Questions often combine a force analysis with an energy or momentum calculation.
Core rules
- For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
- The gradient of a displacement-time graph is velocity; the gradient of a velocity-time graph is acceleration; the area under a velocity-time graph is displacement.
- Newton's second law: resultant force F = ma. Resolve forces along and perpendicular to the motion.
- Impulse = Ft = change in momentum. Momentum is conserved in an isolated system.
- Work done W = Fs cos θ; kinetic energy = ½mv²; gravitational potential energy change = mgh; power P = Fv.
Worked example
A 2.0 kg trolley moving at 3.0 m s⁻¹ collides with a stationary 1.0 kg trolley and they move together. Find the common velocity and the kinetic energy lost. Momentum before = 2.0 × 3.0 = 6.0 kg m s⁻¹. After collision: (2.0 + 1.0)v = 6.0, so v = 2.0 m s⁻¹. Initial KE = ½ × 2.0 × 3.0² = 9.0 J. Final KE = ½ × 3.0 × 2.0² = 6.0 J. Loss = 3.0 J. The loss is consistent with a perfectly inelastic collision; momentum is conserved but kinetic energy is not.
Traps
Using sign conventions inconsistently; forgetting the normal reaction when finding friction; applying conservation of momentum to a system with an external resultant force; confusing work done by and against friction; using P = Fv when v is not along F.