2RearrangingOne of the tasks that physics requires is being able to rearrange equations.Remember:The reason for rearranging is to isolate the variable that you are looking for.Basic Rule: What you do to one side of the equation, you must do to the other side also.
3Example: v = d/t Solve for d Multiple both sides by t. The t’s on the right hand side cancel leaving d.Therefore, d = vtSolve for tAgain, multiply both sides by t and divide both sides by v.Therefore, t = d/v
4Example: d = ½ g t2 Solve for time. Multiple both sides by 2 2d = gt2 Divide both sides by g2d/g = t2Square root both sides.T = √(2d/g)
5Example: E = mgh + ½ mv2 Solve for m E = m(gh + ½ v2) m = E/(gh + ½ v2)
6Example 2: E = mgh + ½ mv2 Solve for h E – ½ mv2 = mgh
7Example 3: E = mgh + ½ mv2 Solve for v E – mgh = ½ mv2
8Example 4: Solve by Substitution 2x + 8y = 1Unsolvable on its own….x = 2yBut if two equations are known…Solve for x and ySince x = 2y, you can insert 2y wherever x occurs.Now you can solve for x:2(2y) + 8y = 14y + 8y = 112y=1y = 1/12x = 2yy = 1/12x = 2(1/12)y = 1/6
9Describing Motion Motion can be described using words. Motion can be described using diagrams.Motion can be described using equations.Motion can be described using graphs.
10Vocabulary: Scalar vs. Vector A scalar quantity has magnitude only.Examples: distance, temperatureA vector quantity has magnitude and direction.Examples: force, acceleration.Symbols for vector quantities are written in bold or with an arrow above them:
11Distance vs. Displacement Beginning Question:A teacher walks 5.0m north of his desk, and then turns around and walks 6.0m south. How far has the teacher gone?11.0m? … or 1.0m?“How far has he gone” is not clear enough.We need to distinguish betweenDistance vs. Displacement
12Vocabulary: Distance: How far an object has traveled A scalar quantity: has magnitude only.Displacement: Change in positionA vector quantity: has magnitude and direction.
14Motion can be described using words. Motion can be described using diagrams.Motion can be described using equations.Motion can be described using graphs.…but always depends on a FRAME OF REFERENCE.…………………..assign a coordinate system.
15Sample problem #1A teacher walks 5.0m north of his desk. What is the teacher’s displacement?The desk is at xi = 0.0mThe teacher’s final position, xf = 5.0m northThe displacement, Dx = xf – xiDx = 5.0m – 0.0mDx = 5.0m
16Sample problem #2Find the displacement of the gecko.
17Sample problem #3Find the displacement of the gecko.
18If a displacement is written without a direction stated, assume it is in the x – direction.eg: d = 54.9 m
19Sample problem #4A teacher walks 5.0m north of his desk. He then walks 6.0m south. What is the teacher’s displacement in reference to his desk? What is the total distance the teacher has walked?Forget about the formula and think this through.If north is positive and south is negative, thenDx = 5.0m – 6.0m = -1.0mor 1.0m south of the desk
20Sample problem #4A teacher walks 5.0m north of his desk. He then walks 6.0m south. What is the teacher’s displacement in reference to his desk? What is the total distance the teacher has walked?Distance = total amount traveledDistance = 5.0m + 6.0m = 11.0m walkedNotice how the direction is not considered.
25How fast is an object moving? Average Velocity: vdisplacement : time ratioA vector quantity: has magnitude and direction.total displacement : total time elapsedAverage Speed:distance : time ratioA scalar quantity: has magnitude and direction.total distance : total time elapsed
27Velocity vs. Speed Velocity is a vector Velocity = displacement time Speed is a scalar (direction does not matter)Speed = distance
28Speed and VelocityCan an object have a velocity that is changing while the speed remains the same?Can an object have a speed that is changing while the velocity remains the same?
29Instantaneous Velocity Constant VelocityConstant velocity is when an objects velocity remains the same for a given amount of time.Instantaneous VelocityInstantaneous velocity is the velocity at a given point in time.Example: Speedometer, Radar gun
30Sample Problem #5 Suzy Physics Student lives 5.0miles south of school. If she takes 2.0 hours to get to school, what is Suzy’s average velocity?
31Sample Problem #6 Suzy Physics Student walks 5.0miles South to school. She takes 2.0 hours to get to school, realizes she is hungry and decides to walk for 1.0 hour to go 2.0 miles North to IHOP.What is Suzy’s average velocity for the whole trip?What is Suzy’s average speed for the whole trip?
38Linear Relationships: y = k x Slopem=(40-8)/(50-10)m=32/40m=0.8 g/cm3Interpolationvs.Extrapolation
39Graphing Motion Motion can be described using words. Motion can be described using diagrams.Motion can be described using equations.Motion can be described using graphs.
40Graphing Motion Graphs of Position vs. Time Calculate the displacement Calculate the velocityDescribe forward and reverse motionDescribe an object staying still
41Calculating displacement A position vs. time graph lets you calculate the displacement between any two moments:x, Position, (m)t, Time, (s)
42Calculating displacement Find the displacement between A and Bx, Position, (m)B (1,5)Dx = xf – xiDx = 5m – 0mDx = 5mUse Dx = xf –xiWhere xf = 5mand xi = 0mt, Time, (s)A (0,0)
43Calculating displacement Find the displacement between C and Dx, Position, (m)C (4,8)Use Dx = xf –xiWhere xf = 3mand xi = 8mDx = xf – xiDx = 3m – 8mDx = -5mD (8,3)t, Time, (s)
44Calculating displacement Find the displacement from when the object was moving for 2s to when it had been moving for 9s.x, Position, (m)6mDx = xf – xiDx = 6m – 5mDx = 1mUse Dx = xf –xiWhere xf = 6mand xi = 5m5mt, Time, (s)2s9s
51Acceleration Motion can be described using words. Motion can be described using diagrams.Motion can be described using equations.Motion can be described using graphs.
52Acceleration vs. Acceleration TermsAcceleration vs. AccelerationAcceleration: The rate at which velocity changes (vector)Acceleration: The rate at which speed changes (scalar)Symbol: a or aSI Unit: meters per second per second or meters per second squared, m/s/s or m/s2
63Falling Bodies, thrown up objects, and the y-direction All things fall at the same rate (neglecting air resistance)On earth that rate is 9.80 m/s2That rate is an accelerationThe name of that acceleration is Gravity