Chapter 2. Motion along a straight line

Transcription

1 Chapter 2 Motion along a straight line

2 Motion We find moving objects all around us. The study of motion is called kinematics. Examples: The Earth orbits around the Sun A roadway moves with Earth s rotation

3 2.2 Motion Here we will study motion that takes place in a straight line. Forces cause motion. We will find out, as a result of application of force, if the objects speed up, slow down, or maintain the same rate. The moving object here will be considered as a particle. If we deal with a stiff, extended object, we will assume that all particles on the body move in the same fashion. We will study the motion of a particle, which will represent the entire body.

4 2-1 Position, Distance, and Displacement Before describing motion, you must set up a coordinate system define an origin and a positive direction.

5 2-1 Position, Distance, and Displacement The distance is the total length of travel; if you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi.

6 2-1 Position, Distance, and Displacement Displacement is the change in position. If you drive from your house to the grocery store and then to your friend s house, your displacement is 2.1 mi and the distance you have traveled is 10.7 mi.

7 2-2 Average Speed and Velocity The average speed is defined as the distance traveled divided by the time the trip took: Average speed = distance / elapsed time Is the average speed of the red car 40.0 mi/h, more than 40.0 mi/h, or less than 40.0 mi/h?

8 2-2 Average Speed and Velocity Average velocity = displacement / elapsed time If you return to your starting point, your average velocity is zero.

9 2-3 Instantaneous Velocity Definition: (2-4) This means that we evaluate the average velocity over a shorter and shorter period of time; as that time becomes infinitesimally small, we have the instantaneous velocity.

10 2-3 Instantaneous Velocity This plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity is tangent to the curve.

11 2-3 Instantaneous Velocity Graphical Interpretation of Average and Instantaneous Velocity

12 2-4 Acceleration Average acceleration: (2-5)

13 2-4 Acceleration Graphical Interpretation of Average and Instantaneous Acceleration:

14 2-4 Acceleration Acceleration (increasing speed) and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration:

15 2-5 Motion with Constant Acceleration When the acceleration is constant, its average and instantaneous values are the same. If the acceleration is constant, the velocity changes linearly: Average velocity: (2-7)

16 2-5 Motion with Constant Acceleration Average velocity: (2-9) Position as a function of time: (2-10) (2-11) Velocity as a function of position: (2-12)

17 2-5 Motion with Constant Acceleration The relationship between position and time follows a characteristic curve.

18 2-5 Motion with Constant Acceleration

19 2-6 Applications of the Equations of Motion Hit the Brakes!

20 2-7 Freely Falling Objects Free fall is the motion of an object subject only to the influence of gravity. The acceleration due to gravity is a constant, g.

21 2-7 Freely Falling Objects An object falling in air is subject to air resistance (and therefore is not freely falling).

22 2-7 Freely Falling Objects Free fall from rest:

23 2-7 Freely Falling Objects Trajectory of a projectile:

24 Summary of Chapter 2 Distance: total length of travel Displacement: change in position Average speed: distance / time Average velocity: displacement / time Instantaneous velocity: average velocity measured over an infinitesimally small time

25 Summary of Chapter 2 Instantaneous acceleration: average acceleration measured over an infinitesimally small time Average acceleration: change in velocity divided by change in time Deceleration: velocity and acceleration have opposite signs Constant acceleration: equations of motion relate position, velocity, acceleration, and time Freely falling objects: constant acceleration g = 9.81 m/s 2