Chapter 2

Motion in One Dimension1. Speed2. Displacement3. Average and Instantaneous velocity4. Acceleration5. Motion Diagrams6. 1D motion with constant acceleration7. Law of falling body

Dynamics What is Dynamics? What is Kinematics?

Objects in Motion How does one describe motion?

Position and Displacement Position

Definition Representation Units

Displacement Definition Representation Units

Difference between displacement and distance

Vector and Scalar Quantities What are vectors? Why do I need them? How do I represent them

During problem solving on paper On Diagrams

Speed and Velocity Average Speed

Definition Calculation Units

Average Velocity Definition Calculation Units

Difference between speed and velocity

Finding Average Velocity on graphs

Instantaneous and Uniform Velocity Definition What is it? How do I

calculate it from graph?

What is uniform velocity?

Example A toy train moves

slowly along a straight portion of track according to the graph of position versus time shown. Find a) the average velocity of the total trip, b) the average velocity during the first 4.0s of motion, c) the instantaneous velocity at t=9.0s

Acceleration Definition Representation Units Average acceleration Instantaneous acceleration Uniform acceleration Graphical interpretation

Graphical Interpretation

ExampleA baseball player

moves in a straight-line path in order to catch a fly ball hit to the out field. His velocity as a function of time is shown. Find his instantaneous acceleration at points A, B and C.

Relationship Between Acceleration and Velocity

Kinematic Equations Used in situations with uniform

acceleration

2

2 2

1212

2

o

o

o

o

v v at

x vt v v t

x v t at

v v a x

Example

A bus moving at a speed of 40 m/s begins to slow at a rate of 3 m/s each second. Find how far it goes before stopping?

Example

An object starts from rest with constant acceleration of 10 m/s2 along a straight line. Find a) the speed at the end of 5 seconds, b) the average speed at the 5 second interval, c) the distance traveled in 5 seconds.

Graphical Interpretation of the Equation

Galileo Galilee 1564 - 1642 Galileo formulated

the laws that govern the motion of objects in free fall

Also looked at: Inclined planes Relative motion Thermometers Pendulum

Free Fall What is the Law of falling body? Galileo's hypothesis Representation Value of g for earth

Estimated value Approximate value Direction of Why g is not a universal constant?

Free Fall – Cases

vo= 0

a = g=-9.8 m/s2

Dropped Thrown downThrown Up

vo≠ 0 & -ve

a = g=-9.8 m/s2

vo≠ 0 & +ve

a = g=-9.8 m/s2

everywhere

v = 0

Symmetric or non-symmetric

Example

A ball is dropped from rest at a height of 50 m above the ground, a) what is the speed just before it hits the ground? b) how long does it take to reach the ground? Ignore air friction

Example

Two rocks are thrown vertically up with a velocity of V and 4V. The ratio of the maximum heights reached (ha/hb) by the rocks is…

Example

Jack and Jill walk down the hill to fetch a pail of water. Jack’s walking path is described by the equation y=0.1x+5 and Jill’s walking path is described by the equation y=0.2x+1. If the source of water is 13 meters away, who reached the river first.