Linear or 1-Dimensional Motion  Mechanics (Physics) = Study of motion of objects, and the related concepts of force and energy.  Kinematics = Description of how objects move without consideration of why they behave or have quantities the way they do (MOTION)  Dynamics = Description or account of why objects move giving them rules/laws (FORCES)  Fundamental Forces of Nature?  Frame of Reference – All measurements are made relative to a frame of reference  Coordinate Systems – Where are objects positioned in reference to origin of coordinates?  Vectors vs. Scalars?

Vectors  A vector quantity can be represented by an arrow-tipped line segment.  The vector has magnitude (size) and direction.

Scalars  A scalar is a quantity with magnitude only.

Distance vs. Displacement  How Far?  The change in position of an object  Example: A person walks 70 meters east, then 30 m west

Speed vs. Velocity  Average Speed – distance traveled divided by the time it takes to travel this distance  Example: Suppose the walk took 80 seconds from the original example? What is the Average Speed?  Average Velocity – Δd/Δt  Instantaneous Velocity – lim Δt –› 0  Example: Suppose the walk took 80 seconds from the original example? What is the Average Velocity?

Working a physics problem Write the givens, labeling the values with appropriate variables Write the base formula with variables only (no numbers!) Re-arrange the formula for the unknown variables (rewrite -- no numbers yet!) Rewrite the formula, substituting the known values for variables in the formula (Check UNITS for any conversions prior to calculating!!!) Box the answer with your work in the final step. Don’t forget the units!!

Example Problems  You are in an awesome boat traveling at 120 km/h over a distance of 90 miles to reach the coast of Cuba. How long does it take you to reach the coast? (1 mi = 1609 m or 1.61 km) express this time in a reasonable unit of time.

Example Problems  A car travels at 30 m/s for a time period of 2.5 hours and then travels 25 m/s for an additional time of 4.0 hours. How far will this car be from its starting point, in kilometers, at the end of the journey?

Example Problems  During your drive home you travel a stretch of road at the rate of 25 km/h for 4.0 minutes, then at 50 km/h for 8.0 minutes and finally at 20 km/h for 2.0 minutes. Find the average speed for the complete trip in m/s. (10.7 m/s)

Accelerated Motion  What do we call it when we change velocity?  Acceleration  a =  v/  t  What does the  mean?  Change  So, a = (v f – v o )/ t

Displacement formula  To find displacement we use these two formulas v = d/t v = (v f + v 0 ) / 2 d = v * t d = [(v f + v 0 )/2]t d = ½ (v f + v 0 )t

Displacement formula  What if we didn’t know v f and we still wanted to know displacement? d = ½ (v f + v o )tvf = v o + at d = ½ [(v o + at) + v o ]t d = v o t + ½at 2

Displacement formula pre-ap What does the area of the green box represent? How do you find the area for the red section? v * t = d displacement ½ base * height or ½ t(v f -v o ) v0v0 vfvf

Displacement formula What is the area of the green and red sections? vovo vfvf d = v 0 t + ½ t(v f – v 0 ) v f = v 0 + at at = (v f – v 0 ) d = v 0 t + ½ at 2

Displacement formula  What if we didn’t know time and we still wanted to know displacement? v f = v 0 + at t = v f –v 0 / a d = v 0 t + ½at 2 d = v 0 [(v f -v 0 )/a] + ½ a[(v f -v 0 )/a] 2 v f 2 = v ad

Big box of formulas d = ½ (v f + v 0 )t d = v 0 t + ½at 2 v f 2 = v ad v f = v 0 + at

Example Problems  A jumbo jet taxiing down the runway receives word that it must return to the gate to pick up an important passenger who was late to his connecting flight (this never happens anymore). The jet is traveling at 45 m/s when the pilot receives the message. What is the acceleration of the plane if it takes the pilot 5 s to bring the plane to halt?

Example Problems  If a dragster car racer car guy from a Tokyo drift movie was in a race for like something cool. What would his acceleration be if he traveled 155 m in 20 s?

Example Problems

What is free fall?  Something falling through the air as a result of gravity.  How fast does it fall? -9.8 m/s 2 (Should we test this?)  What does the negative sign tell you? Direction

Make a list of everything you might be asked about something in free fall:  How fast is it falling?  Initial and final?  How far did it fall?  How long was it in the air?  What variables are represented in the above questions?  a, v f, v 0, d, t

How fast meaning acceleration?  Gravity = -9.8 m/s 2  What is the formula for acceleration?  v f = v 0 + at

How fast meaning final velocity?  v f = v o + at  What type of velocity is this, average or instantaneous?

If you drop a ball from rest what is it’s velocity 1s later?  t = 1 s  vi = 0 m/s  vf = ?  a = -9.8 m/s 2  Show your work

Make a data table Time (s) v f (m/s)

How far?  At the end of 1 second the instantaneous speed is 10 m/s  Does this mean it fell 10 m in the first second?  NO  It did not average 10 m/s for the whole first second. The velocity at the end of the first second was 10 m/s.  We need to know the average speed during the first second in order to find out how far it fell.

How could you find the average speed between 0 and 10 m/s?  Mathematically how do you find an average?  Add up the numbers and divide by how many you have.  (v o + v f ) / 2  Therefore ( m/s) / 2 = 5m/s  So the ball averaged 5 m/s during the first second and fell 5 m

Make a data table Time (s) v f (m/s) Distance (m)