Good Morning/

Afternoon

• Turn in: Graphs w/ analysis

• Get ready for some notes

• HW: pg. 78-79: 2-4, 9, 10; pg. 82: 1, 3, 6, 7, 14 (OpenStax College Physics Book… the one online)

KINEMATICS

Objects in motion…

Needed Skills

•Right triangle trigonometry

•Unit Conversion

•Graph interpretation

ONE DIMENSIONAL

MOTION

Classical Mechanics

• Objects are large and move relatively slow (v<<c)

• Consider all objects as particles

– A particle is a point-like mass having infinitesimal size and finite mass.

• Objects do not rotate

S.I. Units •Remember we have to use proper S.I. (metric) units:

–Meters (m)

–Seconds (s)

–Kilograms (kg)

Kinematics • Study of motion with no regard to its causes.

• Objects move or do not move, accelerate or do not accelerate and we do not care why.

• First we’ll look at objects in motion in one-dimension

• Later we’ll introduce two-dimensional motion

Scalars vs. Vectors

• Scalar – quantities with magnitude (size) and units

• Vector – quantities with magnitude (size), units, and direction

Distance • The distance of a particle is defined as the total length of the path traveled.

• Distance is SCALAR– Always positive no matter which

way you move

• S.I. unit of meters (m)

Sample An object moves from x = 2 m to x = 5 m, stops and turns around traveling then to x = -2 m. What is the total distance the object travels?

Displacement

• The displacement of an object is defined as its change in position.

• In other words, how far does it end up from where it began?

– Change in anything is final - original

• Displacement is a VECTOR– Depends on the direction relative to

some reference point.

• S.I. unit of meters (m)

Physicists consider motion to the right as positive and

motion to the left as negative.

∆ 𝑥=𝑥 𝑓 −𝑥𝑜

Sample An object moves from x = 2 m to x = 5 m, stops and turns around traveling then to x = -2 m. What is the total displacement of the object?

Sample A sprinter is to run the 400 m dash. If the starting line is where the finish line is, what is the total distance the runner travels and what is their displacement?

Speed • Average speed is defined as

• Speed is scalar so is always positive

• S.I. derived unit of

𝐴𝑣𝑒𝑟𝑎𝑔𝑒𝑠𝑝𝑒𝑒𝑑=𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑡𝑜𝑡𝑎𝑙𝑡𝑖𝑚𝑒

Sample A car travels 4000 m in 10 min. What is the average speed of the car?

Sample A car is to travel 3000 km in 30 hrs. If you complete the first 1500 km of the trip averaging 75 km/hr, what must be your average speed for the second half of the trip?

Note: Since the distance, time, and speed have matching units we do not need to convert unless asked to.

Average Velocity

• Average velocity is defined as the displacement of the object over the time needed for the displacement.

• Velocity is a vector so it required direction.

• S.I. derived unit of

• The average velocity is truly defined as the average of the final and original velocities.

𝑣𝑎𝑣𝑔=∆ 𝑥𝑡

𝑣𝑎𝑣𝑔=𝑣 𝑓 +𝑣02

DIRT? •Remember d=rt?

•Now its –(avg. velocity equation)

Steps for Solving Rate Problems:

1.Diagram/Set-up reference point.

2.Set up equation(s).3.Solve for unknowns.

Sample Two locomotives approach each other on parallel tracks. Each has a speed of 95 km/hr with respect to the ground. If they are initially 9.5 km apart, how long will it be before they reach each other?

Sample Dr. Sandomir is out for a morning walk in the woods. A bear, 20 m behind him, starts to give chase to Dr. Sandomir, running at 3.0 m/sec. The fastest Dr. Sandomir can run is 0.5 m/sec. If Dr. Sandomir can JUST dive into his car as the bear is catching up to him, how long did it take the bear to catch him AND how far was Sandomir from the car when the bear gave chase?

Sample A bowling ball traveling with constant speed hits the pins at the end of a bowling lane 16.5 m long. The bowler hears the sound of the ball hitting the pins 2.5 sec after the ball is released from his hands. What is the speed of the ball? The speed of sound is 340 m/sec.

Happy Hump Day!

• Get out notes… let’s do this!

• Tomorrow: Constant Velocity Lab

• HW: Position Time Graphs WS

Position Time

Graphs

Position Time

Graphs

• The slope of a position time graph:

– Units: (units for velocity)

• Constant slope = constant velocity

• “Curved” (Parabolic) slope = changing velocity

Sample Given the graph to the left, determine the following:

a) Total distance traveled and average speed from A to G.

b) Average velocity for sections AB, BC, CD, DE, EF, FG.

c) Average velocity from A to G.

Sample a) Given the graph below, determine the average velocity for the entire trip from t = 0 – 5 seconds.

b) What direction is this object moving in?

c) Is this object moving at a constant velocity, speeding up, or slowing down?

Throw Back

Thursday

• Make sure you turned in everything from yesterday

• NOTE: If you need me at lunch I will be in the Chemistry office in room 118. Feel free to come find me.

• Stem Club Informational Meeting On Tuesday after school

• Today we talk about ACCELERATION!

• HW: pg. 79: 13, 14, 17; pg. 80-81: 27, 30; pg. 82-83: 19, 22, 27, 32, 34

– Remember to use the PDF version!

Warm Up: • Determine the average velocity in each section.

• Determine the average velocity overall.

Accelerated Motion

• Acceleration is defined as the rate change in velocity:

𝑎= ∆𝑣𝑡

=𝑣𝑓 −𝑣𝑜

𝑡

Since acceleration depends on the change in velocity, one (or a combination) of the following can cause can acceleration: 1. Speeding up in one direction2. Slowing down in one direction3. Changing direction at constant

speed

Velocity Time

Graphs

• The slope of a velocity time graph represents…

• Slope of a velocity-time graph = acceleration

• Unit analysis:

(units for acceleration)

Velocity Time

Graphs

• The area beneath a velocity time graph represents…

• Unit analysis:

• Meters are a unit of displacement

• Area underneath velocity-time graph = displacement

Velocity Time

Graphs

True or false:

1.A car must have an acceleration in the direction of its velocity.

2.It is possible for a car to slow down while having positive acceleration.

Velocity Time

Graphs

• Let’s analyze the graph at the left:

But

So

∆ 𝑥=𝑣𝑜𝑡+12𝑎𝑡 2

Sample A car is moving at 5.0 m/sec when it accelerates at 2.0 m/sec2 for 3.5 sec. Determine the final velocity of the car.

Sample A car is moving at 5.0 m/sec when it accelerates at 2.0 m/sec2 for 3.5 sec. Determine the displacement of the car.

Sample Use the graph to the right to answer the following questions:

1. During which interval is the acceleration the greatest?

2. During which interval is the object moving the positive direction but with a negative acceleration?

3. What is the final displacement of the object?Keep in mind:

1. If the object has the same sign on velocity and acceleration, it is speeding up.

2. If the object has opposite signs on velocity and acceleration, it is slowing down.

The Timeless Equation

• The timeless equation will be used if we are given a problem without “time” information:

Start with:

Use:

but solve for “t”,

Substitute “t”:

Simplify:

2𝑎∆𝑥=𝑣 𝑓2−𝑣𝑜

2

Sample A plane landing on an aircraft carrier hits the deck at 250 m/sec and must stop in 275 m. What minimum acceleration must the plane undergo?

Sample A ball rolling down an incline is moving at 10 m/sec at one point and 3.0 m later is moving at 15 m/sec.

a) What was the rate of acceleration along the incline?

b) How much time did it take to travel the 3.0 m?

c) If it continued this rate of acceleration for one more second, how far would it travel?