Forces, Acceleration and Stopping
Newton's First Law
Newton's First Law states that an object remains at rest, or continues to move at a constant velocity, unless a resultant force acts on it. A resultant force is the single force that represents the combined effect of all forces acting on an object.
If the resultant force is zero, a stationary object stays still and a moving object keeps moving at the same speed in the same direction. If there is a resultant force, the object accelerates — meaning it speeds up, slows down, or changes direction. A spacecraft drifting in deep space, where there is no friction or air resistance, will continue at the same velocity indefinitely unless a thruster fires. This is not because a force is pushing it — it is because no force is acting to slow it down.
Objects do not need a force to keep moving at constant velocity. A resultant force is only needed to change the speed or direction of an object — this is a very common exam misconception.
Newton's Second Law: F = ma
Newton's Second Law tells us that the resultant force on an object equals its mass multiplied by its acceleration:
$$F = m \times a$$
Where \(F\) is force in newtons (N), \(m\) is mass in kilograms (kg), and \(a\) is acceleration in m/s². A bigger force produces a bigger acceleration (if mass stays the same), and a heavier object needs a bigger force for the same acceleration. The equation rearranges to \(a = \frac{F}{m}\) or \(m = \frac{F}{a}\). Always use the resultant force, not any single force in isolation. If a car engine provides 3 000 N but friction and air resistance total 1 000 N, the resultant force is 2 000 N forward.
Question: A 1 200 kg car experiences a resultant force of 3 600 N. Calculate its acceleration.
Step 1: Write the equation: \(a = \frac{F}{m}\)
Step 2: Substitute: \(a = \frac{3600}{1200} = 3 \text{ m/s}^2\)
Now try: A 0.5 kg ball is kicked with a resultant force of 35 N. What is its acceleration? (Answer: 70 m/s²)
Newton's Third Law
Newton's Third Law states: for every action force there is an equal and opposite reaction force. These forces always act on different objects and are always the same type of force. When a swimmer pushes water backwards, the water pushes the swimmer forwards with an equal force. When a rocket expels gases downwards, the gases push the rocket upwards with an equal force.
A common mistake is to confuse a Third Law pair with balanced forces. Balanced forces act on the same object. A Third Law pair always involves forces on different objects. Weight (Earth pulling you down) and normal contact force (ground pushing you up) are NOT a Third Law pair — both act on you. The Third Law pair of your weight is the gravitational pull you exert on the Earth.
Newton's Third Law pairs are always equal in size, opposite in direction, the same type of force, and act on different objects from each other.
Momentum
Momentum is the product of an object's mass and velocity:
$$p = m \times v$$
Where \(p\) is momentum in kg m/s, \(m\) is mass in kg, and \(v\) is velocity in m/s. In a closed system (no external forces), the total momentum before an event equals the total momentum after — this is the conservation of momentum. If a 2 kg trolley moving at 4 m/s collides with and sticks to a stationary 2 kg trolley, momentum before = \(2 \times 4 = 8\) kg m/s. After, the combined 4 kg mass moves at \(\frac{8}{4} = 2\) m/s. Momentum is conserved; kinetic energy is not.
Stopping distance is the sum of two parts:
• Thinking distance — the distance travelled during the driver's reaction time (between seeing the hazard and pressing the brake). Factors that increase thinking distance: tiredness, alcohol, drugs, distractions, higher speed.
• Braking distance — the distance travelled after the brakes are applied. Factors that increase braking distance: higher speed, wet or icy roads, worn tyres, worn or overheated brakes.
Speed has a particularly large effect on braking distance because kinetic energy depends on \(v^2\). Doubling speed quadruples kinetic energy, so the brakes must do four times more work to stop the vehicle — meaning roughly four times the braking distance. This is why motorway speed limits are strictly enforced.
Large braking forces are needed to stop quickly. A very large braking force causes the tyres to skid, reducing control. Modern vehicles use anti-lock braking systems (ABS) to prevent skidding by modulating brake pressure automatically.
Stopping distance = thinking distance + braking distance. Braking distance is proportional to \(v^2\) — doubling speed roughly quadruples braking distance. Speed is the most significant factor in serious collisions.