Kinematics Lecture Notes

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-1 H2 Topic 2 Kinematics Circus stuntmen being shot out of cannons are human projectiles. In the absence of air resistance, they move in parabolic paths until they land in a strategically placed net. Taken from College Physics, Serway/Faughn

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-2 Content • Rectilinear motion • Non-linear motion Learning Outcomes Candidates should be able to: (a) Define displacement, speed, velocity and acceleration. (b) Use graphical methods to represent distance travelled, displacement, speed, velocity and acceleration. (c) Find displacement from the area under a velocity-time graph. (d) Use the slope of a displacement-time graph to find the velocity. (e) Use the slope of a velocity-time graph to find the acceleration. (f) Derive, from the definitions of velocity and acceleration, equations which represent uniformly accelerated motion in a straight line. (g) Solve problems using equations which represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance. (h) Describe qualitatively the motion of bodies falling in a uniform gravitational field with air resistance. (i) Describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction. References: 1 Advanced Level Physics by Loo Kwok Wai 2 College Physics by Young and Geller 3 Physics for Scientist and Engineers (5th Edition) by Serway Physics Tip! To understand Physics, you must be able to understand it (i) Qualitatively – Define, Explain, State, Describe, Discuss, Suggest… (ii) Quantitatively – Calculate, Measure, Determine, Show, Estimate, Suggest… (iii) Graphically – Sketch, Determine, Estimate, Deduce… (iv) Pictorially – Sketch (applied to diagrams) In plain English, you must be able to explain Physics in words, equations & numbers, graphs and diagrams.

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-3 Data speed of light in free space, c = 3.00 × 108 m s-1 permeability of free space, o = 4 × 10-7 H m-1 permittivity of free space, o = 8.85 × 10-12 F m-1 (1/(36)) × 10-9 F m-1 elementary charge, e = 1.60 × 10-19 C the Planck constant, h = 6.63 × 10-34 J s unified atomic mass constant, u = 1.66 × 10-27 kg rest mass of electron, me = 9.11 × 10-31 kg rest mass of proton, mp = 1.67 × 10-27 kg molar gas constant R = 8.31 J K−1 mol−1 the Avogadro constant, NA = 6.02 × 1023 mol-1 the Boltzmann constant, k = 1.38 × 10-23 J K-1 gravitational constant, G = 6.67 × 10−11N m2 kg2 acceleration of free fall, g = 9.81 m s−2 Formulae uniformly accelerated motion, s = ut + 2 1 at2 v2 = u2 + 2as work done on/by a gas, W = pV hydrostatic pressure, p = gh gravitational potential,  = r GM− displacement of particle in s.h.m. x = xo sin t velocity of particle in s.h.m., v = vocost =  22 xxo − mean kinetic energy of a molecule of an ideal gas E = kT2 3 resistors in series, R = R1 + R2 + . . . resistors in parallel, R 1 = 1 1 R + 2 1 R + . . . electric potential, V = r Q o4 alternating current/voltage, x = xo sin t transmission coefficient, T  exp(−2kd) where k = 2 2 )(8 h EUm − radioactive decay, x = xoexp(−t) decay constant,  = 2 1 693.0 t

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-4

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-5

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-6 Not to worry about the approved date. It is up to the vendor to apply to SEAB for approval

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-7

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-8

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-9 Kinematics is a branch of Newtonian (or classical) mechanics concerned with describing the motion of objects without considering factors that cause the motions. In this topic we will concentrate on two types of motion, • Motion along a straight line (Rectilinear motion) • Motion on a plane (Non-linear motion) The following vector and scalar quantities are usually used to describe motion: • Distance (scalar) • Displacement (vector) • Speed (scalar) • Velocity (vector) • Acceleration (vector) 2.1 Rectilinear Motion Learning Outcomes (a) Define displacement, speed, velocity and acceleration. 2.1.1 Distance and Displacement Distance, d The total length of path covered by a moving object irrespective of the direction of motion. Distance is a scalar quantity. Displacement, s The linear distance of the position of the moving object from a given reference point. Displacement is a vector quantity. Considering Figure 1 above, the distance travelled by the particle to move from A to B is the actual length of the irregular path (in bold). The length of the straight line that joins A to B is Figure 1 A B

Dunman High School (Senior High Physics Department) 9646 Physics Topic 2: Kinematics 2-10 the magnitude of the displacement of the particle from A while the arrow provides its direction. Displacement of an object = (displacement of final position from a fixed reference point) – (displacement of initial position from the same reference point) x = x f - x i Graphically: Example 1 Two teams had to travel from Kallang to Marina Bay during an Amazing Race. Team A took the MRT directly from Mountbatten to Marina, while team B took a bus that bypassed City Hall first. What is the distance travelled and the magnitude of the displacement for both teams? Answers: Team A Distance = 10 km Team A Displacement = 10 km Team B Distance = 13 km Team B Displacement = 10 km i = f - i f Reference Point Bus MRT Kallang City Hall Marina Bay Team A Team B 10 km 7 km 6 km initial position final position