Mechanics: Kinematics and Dynamics
What this domain tests
Kinematics and dynamics covers describing motion (distance, displacement, speed, velocity, acceleration, graphs) and explaining it using Newton's laws, resultant forces, friction, moments and circular motion.
Core rules
- Uniform acceleration: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t.
- Gradient of a displacement–time graph = velocity; gradient of a velocity–time graph = acceleration; area under velocity–time = displacement.
- Newton I: no resultant force means constant velocity. Newton II: F = ma. Newton III: equal and opposite forces acting on different bodies.
- Weight W = mg; friction opposes relative motion; the component of weight down an incline is mg sinθ.
- Principle of moments: total clockwise moment = total anticlockwise moment about a pivot.
Worked example
A car travelling at 20 m s⁻¹ brakes uniformly and stops in 4 s. Find the braking distance. First a = (v − u)/t = (0 − 20)/4 = −5 m s⁻². Then s = (u + v)t/2 = (20 + 0)(4)/2 = 40 m. Check with v² = u² + 2as: 0 = 400 + 2(−5)s, giving s = 40 m. Choosing the direction of travel as positive keeps the negative acceleration consistent - a sign slip here is the commonest error.
Traps that cost marks
- Treating distance and displacement, or speed and velocity, as interchangeable.
- Forgetting that a projectile still accelerates downward at g at its highest point.
- Pairing Newton's third-law forces on the same body.
- Averaging two speeds arithmetically when the time intervals are unequal.
- Ignoring the direction of a resultant force when applying F = ma.