Chapter 2 Motion Along a Straight Line

Linear motion In this chapter we will consider moving objects: Along a straight line With every portion of an object moving in the same direction and at the same rate (particle-like motion)

Types of physical quantities In physics, quantities can be divided into such general categories as scalars, vectors, matrices, etc. Scalars – physical quantities that can be described by their value (magnitude) only Vectors – physical quantities that can be described by their value and direction

Distance, position, and displacement Distance (scalar) a total length of the path traveled regardless of direction (SI unit: m) In each instance we choose an origin – a reference point, convenient for further calculations Position of an object (vector) is described by the shortest distance from the origin and direction relative to the origin Displacement (vector) – a change from position x 1 to position x 2

Velocity and speed Average speed (scalar) - a ratio of distance traveled (over a time interval) to that time interval (SI unit: m/s) Average velocity (vector) - a ratio of displacement (over a time interval) to that time interval Instantaneous velocity (vector) – velocity at a given instant Instantaneous speed (scalar) – a magnitude of an instantaneous velocity

Acceleration Average acceleration (vector) - a ratio of change of velocity (over a time interval) to that time interval (SI unit = (m/s)/s = m/s 2 ) Instantaneous acceleration (vector) – a rate of change of velocity at a given instant

Case of constant acceleration Average and instantaneous accelerations are the same Conventional notation Then

Case of constant acceleration Average and instantaneous accelerations are the same Conventional notation Then

Case of constant acceleration

To help you solve problems EquationsMissing variables

Alternative derivation Using definitions and initial conditions we obtain

Case of free-fall acceleration At sea level of Earth’s mid-latitudes all objects fall (in vacuum) with constant (downward) acceleration of a = - g ≈ m/s 2 ≈ - 32 ft/s 2 Conventionally, free fall is along a vertical (upward) y-axis

Graphical representation

Graphical integration

Answers to the even-numbered problems Chapter 2: Problem 12: (a) – 6 m/s. (b) negative x direction (c) 6 m/s (e) Yes (f) No

Answers to the even-numbered problems Chapter 2: Problem 16: 5.9 m

Answers to the even-numbered problems Chapter 2: Problem 28: (a) 2.5 s.

Answers to the even-numbered problems Chapter 2: Problem 42: (a) 3.70 m/s. (b) 1.74 m/s (c) m

Answers to the even-numbered problems Chapter 2: Problem 68: (a) 5.00 m/s (b) 1.67 m/s 2 (c) m (d) - 3 s