What determines how objects accelerate, and how do forces explain motion from braking to projectiles?
Newton's three laws of motion are the foundation of mechanics. The first says that an object at rest stays at rest (or at constant velocity) unless acted on by a resultant force — this is inertia. The second says that the acceleration of an object is proportional to the resultant force and inversely proportional to its mass: F = ma. The third says that forces come in equal and opposite pairs acting on different objects. A common mistake is to confuse third-law pairs (same type of force, opposite directions, acting on different objects) with balanced forces (different types of force, on the same object, summing to zero).
Distance–time and velocity–time graphs are essential tools. The gradient of a d–t graph is speed; the gradient of a v–t graph is acceleration. The area under a v–t graph is distance travelled. Braking distance depends on speed squared — a key reason why speed limits matter. Thinking distance depends on reaction time (affected by tiredness, alcohol, distractions).
A car of mass 1500 kg accelerates from rest to 20 m/s in 8 seconds. (a) Calculate the resultant force. (b) Calculate the stopping distance if thinking distance at this speed is 12 m and braking distance is 24 m. (c) If the driver's reaction time is 0.3 s, what is their thinking distance at 30 m/s?
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