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Lecture Outlines Chapter 2
Physics, 3rd Edition James S. Walker
Chapter 2
One-Dimensional
Kinematics
Units of Chapter 2
• Position, Distance, and Displacement
• Average Speed and Velocity
• Instantaneous Velocity
• Acceleration
• Motion with Constant Acceleration
• Applications of the Equations of Motion
• Freely Falling Objects
2-1 Position, Distance, and Displacement
Before describing motion, you must set up a coordinate system – define an origin and a positive direction.
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.
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.
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?
2-2 Average Speed and Velocity
Checkpoint 2-1
Är medelhastigheten 40,0 mi/h?
t1 = 4,00 mi/(30,0 mi/h) = 0,133 h t2 = 4,00 mi/(50,0 mi/h) = 0,080 h t = t1 + t2 = 0,213 h
medelhastighet = 8,00 mi/0,213 h = 37,6 mi/h
2-2 Average Speed and Velocity
Average velocity = displacement / elapsed time If you return to your starting point, your
average velocity is zero.
2-2 Average Speed and Velocity
Graphical Interpretation of Average Velocity The same motion, plotted one-dimensionally and as an x-t graph:
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.
Table 2-1
x-versus-t Values for Figure 2-7
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.
2-3 Instantaneous Velocity
Graphical Interpretation of Average and Instantaneous Velocity
2-4 Acceleration
Average acceleration:
(2-5)
2-4 Acceleration
Exercise 2-1
Acceleration från stillastående till 60 mi/h (26,8 m/s) på 6,2 s
Ger med nedanstående formel
aav = (26,8 m/s – 0 m/s) /6,2 s = 4,3 m/s2
2-4 Acceleration
Graphical Interpretation of Average and Instantaneous Acceleration:
2-4 Acceleration
Om accelerationen är konstant är
Average Acceleration
identisk med
Instantaneous Acceleration
2-4 Acceleration
Acceleration (increasing speed) and
deceleration (decreasing speed) should not be confused with the directions of velocity and
acceleration:
2-5 Motion with Constant Acceleration
If the acceleration is constant, the velocity changes linearly:
(2-7) Average velocity:
Example 2-3
An Accelerating Train
Figure 2-14
Velocity versus time for the boat in Example 2–5
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)
2-5 Motion with Constant Acceleration
The relationship between position and time follows a characteristic curve.
2-5 Motion with Constant Acceleration
Sista ekvationen mellan v och x (då
accelerationen är konstant) fås med hjälp av (2-7) ger att t = (v-v0)/a som insatt i (2-10)
vav = (x –x0)/(t-0) men vav = (v0 + v)/2 (2-9)
vilket slutligen ger (2-12)
x = x0 + vav t = x0 + (v-v0)(v+v0)/2a x = x0 + (v2 – v02)/2a
2-5 Motion with Constant Acceleration
2-6 Applications of the Equations of Motion
Hit the Brakes!
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.
2-7 Freely Falling Objects
An object falling in air is subject to air
resistance (and therefore is not freely falling).
2-7 Freely Falling Objects
Free fall from rest:
Example 2-10 Do the Cannonball!
Conceptual Checkpoint 2-5 Free-Fall Separation
2-7 Freely Falling Objects
Trajectory of a projectile:
Example 2-11
Bombs Away: Calculating the Speed of a Lava Bomb
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
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/s2
