Mechanics, Forces and Motion
Motion
Speed = distance ÷ time. Velocity is speed in a given direction, and acceleration = change in velocity ÷ time. On a distance–time graph the gradient is speed; on a velocity–time graph the gradient is acceleration and the area under the line is distance travelled. Deceleration is negative acceleration.
Forces and Newton's laws
Balanced forces produce no change in motion; unbalanced forces cause acceleration. Newton's second law: resultant force = mass × acceleration (F = ma). For every action there is an equal and opposite reaction. Weight is the force of gravity: W = mg, where g is about 10 N/kg on Earth. Friction and air resistance oppose motion, and terminal velocity is reached when air resistance equals weight.
Moments, pressure and density
For a lever in equilibrium, clockwise moments = anticlockwise moments; moment = force × perpendicular distance from the pivot. Pressure = force ÷ area, and liquid pressure increases with depth. Density = mass ÷ volume. Hooke's law states that extension is proportional to force up to the limit of proportionality: F = kx.
Worked example
A car accelerates uniformly from 0 to 20 m/s in 5 s. Acceleration = (20 − 0) ÷ 5 = 4 m/s2. The distance travelled is the area under the velocity–time graph: a triangle with area ½ × 5 × 20 = 50 m.
Traps that cost marks
Mass and weight are different: mass is in kg and weight in newtons. On a velocity–time graph, the gradient is acceleration, not speed. Use perpendicular distance for moments. Convert units before calculating.