Chapter 2 Motion in One Dimension

Dynamics Dynamics: branch of physics describing the motion of an object and the relationship between that motion and other physics concepts Kinematics is a part of dynamics. In kinematics we are interested in the description of motion, without the description of the cause of the motion Any motion involves three concepts used to study objects in motion: 1) Displacement 2) Velocity 3) Acceleration

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 i to position x f

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

Velocity and speed

Instantaneous velocity The instantaneous velocity is the slope of the line tangent to the x vs. t curve This would be the green line The light blue lines show that as Δt gets smaller, they approach the green line

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

Acceleration The blue line is the average acceleration The slope (green line) of the velocity-time graph is the acceleration

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

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

Case of constant acceleration To help you solve problems EquationsMissing variables

Case of constant acceleration

Graphical representation

Chapter 2 Problem 36 A car accelerates uniformly from rest to a speed of 40.0 mi/h in 12.0 s. Find (a) the distance the car travels during this time and (b) the constant acceleration of the car.

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

Chapter 2 Problem 45 A certain freely falling object requires 1.50 s to travel the last 30.0 m before it hits the ground. From what height above the ground did it fall?

Questions?

Answers to the even-numbered problems Chapter 2 Problem 4: 12.2 mi/h

Answers to the even-numbered problems Chapter 2 Problem 8: (a) 2.3 min (b) 64 mi

Answers to the even-numbered problems Chapter 2 Problem 16: (a) 41.0 m/s, 41.0 m/s, 41.0 m/s (b) 17.0 m/s, much less than the results of (b)

Answers to the even-numbered problems Chapter 2 Problem 20: 0.75 m/s 2

Answers to the even-numbered problems Chapter 2 Problem 32: (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km

Answers to the even-numbered problems Chapter 2 Problem 50: (a) 2.3 s (b) - 33 m/s