PhysicsChapter Two - Kinematics

Presented by: Taylor Ripke

Mechanics- Study of Motion Kinematics- Mechanics of Objects

**Assume no rotation** Ex. Cars, Atoms, Planes

Section 2.2 - Kinematics

Position Vector – Where it is Denoted by: r Changes as a function of time r = r (t)

Position and Displacement Vectors

Definition: Difference between final position vector and initial position vector

∆r = r2 – r1

∆r means “difference or change in”

Displacement

**Not the same as Displacement** Recall displacement- how far from origin Definition: Absolute value of the displacement

vector “How far you’ve traveled” Δr = |r1| + |r2|

Distance

Your dorm room is located 0.25 mi from the dairy store. You walk from your room to the Dairy Store and back. Which of the statements is true:

a) The distance is 0.5 mi and displacement is 0.5 mi.

b) The distance is 0.5 mi and displacement is 0.0 mi.

c) The distance is 0.0 mi and displacement is 0.5 mi.

Example

Example ContinuedHome Dairy Store0.25mi

Displacement = ∆r = r2 – r1 = 0.25 – 0.25 = 0mi

Distance = Δr = |r1| + |r2| = |0.25| + |0.25| = 0.5mi

If ri = rf, displacement is 0.

Displacement = How far from origin

Distance = Total ground covered

Key Points

Section 2.3 - Velocity Average velocity – Vx = Instantaneous velocity – V = Speed – absolute value of velocity

Velocity – a vector with direction

**Speed is never negative**

Speed = |v| = |vx|

Average speed = v =

“ ” 𝑙 being distance

Equations

Suppose a swimmer completes the first 50m of the 100m freestyle in 38.2s. She then turns around and swims back in 42.5s.

Question: What is the average velocity and average speed for the first leg?

Example

Vx = = = = 1.31

Average velocity = 1.31Speed is the absolute value = |1.31| = 1.31

Solution

Average acceleration – defined as the velocity change per time interval

ax =

Instantaneous acceleration – defined as the limit of the average acceleration as the time interval approaches 0.

Acceleration

Graph Representations

Average Velocity/Acceleration

Instantaneous Velocity/Acceleration

I.

Fundamental Kinematic Equations

Assuming a constant acceleration of ax = 4.3 m/s2, starting from rest, what is the airplane’s take off velocity after 18.4s?

Example

I. Find an equation

II. At Rest

III. Acceleration

IV. Time

Solution

Displacement – how far from origin Distance – how far you’ve traveled Velocity – vector with direction Speed – absolute value of velocity Acceleration – velocity change with time

Recap

• Campus Party Brasil, “Michio Kaku” February 11, 2012 via Flickr, Attribution-ShareAlike

• Ed Schipul, “Bill Nye” October 21, 2010 via Flickr, Attribution-ShareAlike

• Bauer, W., & Westfall, G. (2014). University physics (Second ed.). New York, NY: McGraw-Hill.

References