Distance is a scalar quantity: length of the route covered by an object. (p.26)
Displacement is a vector quantity: shortest distance between initial and final position in a specific direction. (p.26)
Speed = distance travelled / time taken; v = d/t (p.28)
Velocity = displacement / time taken; v = s/t (p.28)
Acceleration = (final velocity − initial velocity) / time; a = (v − u)/t (p.28)
A ticker timer works on alternating current of frequency 50 Hz: 1 tick = 0.02 s. (p.30)
Linear Motion Equations (constant acceleration)
v = u + at (p.35)
s = ½(u + v)t (p.35)
s = ut + ½at2(p.35)
v2 = u2 + 2as (p.35)
2.2 Linear Motion Graphs
Displacement–time graph: gradient of the graph = velocity. (p.37)
Velocity–time graph: gradient of the graph = acceleration; area under the graph = displacement. (p.37)
2.3 Free Fall Motion
Free fall: motion of an object affected only by gravitational force (no air resistance). (p.46)
Average gravitational acceleration, g ≈ 9.81 m s−2; g = 9.78 m s−2 at the equator; g = 9.83 m s−2 at the poles. (p.47)
Determining g experimentally: g = 2h / (t22 − t12) (p.48)
Equations for vertical motion: v = u + gt; s = ut + ½gt2; v2 = u2 + 2gs (p.50)
2.4 Inertia
Inertia is the tendency of an object to remain at rest or, if moving, to continue its motion in a straight line at uniform velocity. (p.52)
Newton's First Law of Motion: an object will remain at rest or move at uniform velocity unless acted upon by an external force. (p.52)
The larger the mass of an object, the larger its inertia. (p.54)
Daily-life effects of inertia: seat belts, compartmentalised oil tanker trucks, roller coaster safety systems, the table-cloth trick. (p.56)
2.5 Momentum
Momentum, p = mv. S.I. unit: kg m s−1 (= N s). (p.58)
Principle of Conservation of Momentum: m1u1 + m2u2 = m1v1 + m2v2 (when no external force acts). (p.62)
Applies to explosions too, e.g. rocket launch: m1v1 = −m2v2. (p.63)
2.6 Force
Newton's Second Law of Motion: the rate of change of momentum of an object is directly proportional to the applied force and acts in the direction of the force. (p.65)
F = ma. (1 N is the force that produces an acceleration of 1 m s−² on a mass of 1 kg.) (p.65)
2.7 Impulse and Impulsive Force
Impulse, J = mv − mu = Ft (p.67)
Impulsive force, F = (mv − mu)/t (p.67)
Newton's Third Law of Motion: for every action there is a reaction of equal magnitude but in the opposite direction. (p.68)
Examples: follow-through in football increases impulse; car crumple zones extend impact time to reduce impulsive force; a mortar and pestle reduce impact time to increase impulsive force. (p.68)
2.8 Weight
Weight, W = mg (p.70)
Gravitational field strength, g (unit: N kg−¹), is the force acting per unit mass due to gravitational pull. On Earth's surface, g = 9.81 N kg−¹. (p.70)
The Moon's gravitational field strength is about 1/6 of Earth's. (p.71)