Kinematics Kinematics comes from the Greek word kinein, meaning to move. We can describe motion in three ways: 1.Sentences 2. Mathematical quantities 3. Graphs that show how these quantities change in time. If it takes Mr. Redmond 25 minutes to travel to school (a distance of 18 km) how fast does he travel? = 0.72 km/min (2 sig figs) 0.72km in 1 minute Let’s change units to km/h and m/s. × = 43.2 km/h = 43 km/h (2 sig figs) × × = 12 m/s Try This: What is your speed traveling to school? Express your answer in 3 different units of speed. Do we always move at this speed? NO! This is an AVERAGE speed!! When Mr. Redmond was coming up to the bridge tolls his speed reduced to 20km/h for the MacPass lane. This speed is an INSTANTANEOUS speed.
Transcript
Kinematics
Kinematics comes from the Greek word kinein, meaning to move.
We can describe motion in three ways:1. Sentences2. Mathematical quantities3. Graphs that show how these quantities change in time.
If it takes Mr. Redmond 25 minutes to travel to school (a distance of 18 km) how fast does he travel?
= 0.72 km/min (2 sig figs)0.72km in 1 minute
Let’s change units to km/h and m/s.
× = 43.2 km/h = 43 km/h (2 sig figs)
× × = 12 m/s
Try This: What is your speed traveling to school? Express your answer in 3 different units of speed.
Do we always move at this speed? NO! This is an AVERAGE speed!!
When Mr. Redmond was coming up to the bridge tolls his speed reduced to 20km/h for the MacPass lane. This speed is an INSTANTANEOUS speed.
What is speed? The rate at which distance is traveled (How much
distance changes over time). Speed is a scalar measurement it only has magnitude
(amount).
In Physics, we need to be more precise. We use VECTORS to include magnitude and direction. Velocity is the vector of speed.Examples of
Scalars Vectors
Time VelocityEnergy ForcesSpeed AccelerationDistance DisplacementMass Weight
Note: Displacement is an objects change in position relative to the reference point (where it started).Distance is an objects total distance traveled.
Finding average velocity:
A ball is thrown into the air. Its data is as follows;Time (s)
2. What is the average velocity from t = 0s – 3.0s?
= = = 2.2m/s
3. What is the average velocity from t = 3.0s – 5.0s?
= = = = -2.5m/s
Why the negative sign? Because the ball is traveling down
4. What is the average speed from t = 3.0s – 5.0s?s = 2.5m/s NO DIRECTION
RecapVelocity =
=
Displacement is the change in position of an object, d.
Example #1:A train travels averaging a velocity of +227km/h. Your trip takes
2.00h. How far did you go?
= Undo BEDMAS first, and then sub in #’st = (t)
= t=(+227km/h)(2.00h)
= 454kmAlways use units!!!!
A closer look at displacement!
Jenn walks 45m EAST, then 31m WEST. What is her:a. distance traveled?b. displacement? (change in position)
a. Distance is a scalar NO Directionno arrow d = 45m + 31m = 76m
b. Displacement includes direction ‘+’ is East‘─’ is West
= +45m + (─31m) = +14m or 14m East
Displacement-Time Graphs• before you can study how something moves, we need to know where it is.
• describe position in terms of its relationship to some other point. Using a scale, 0 would become our reference point.
• when you make 0 the reference point, you have chosen a frame of reference.
• the position of an object is the separation between that object and a reference point.
• distance does not require a frame of reference (direction is not important).
• use +, - to describe position.
What information can you find on a d-t graph? velocity
If the displacement is the vertical separation and time is the horizontal separation, the slope = Δd/Δt
POSITION-TIME GRAPHS
Sean’s trip to school today started with him walking 950m West in 7.5 minutes to pick up a friend. When he met up with Melissa, they stopped to chat for about 4.5 minutes. They took 20.0 minutes to walk 1050m East back to school. Draw their corresponding position-time graph and answer the following questions.
1) For how many minutes was Sean walking?2) What is the school’s position relative to Sean’s house?3) What is Sean’s displacement over the following intervals?
a. t = 0 – 9 min b. t = 11 – 32 min
4) What was Sean’s velocity as he walked by himself?5) When did they pass Sean’s house?
Describe the motion of the object in sentences and quantify the position and velocity.
Positive and Negative Velocities
• positions can be positive or negative.• velocities can be positive or negative.
Example:A player is on the +20m line and runs 10 m/s. Where will the player end up?
+30m line+10m line
If the magnitude of the velocity is 10 m/s you need to assign a direction.If the player runs - 10 m/s, they will end up on the + 10m line.
• negative velocity means DIRECTION not speeding up or down.
Instantaneous Velocity
an object does not always move at a constant speed. you may speed up or slow down.
when you are driving on the highway and you look down at your speedometer, you are traveling at +55 km/h. At that instant in time, +55 km/h is your instantaneous velocity.
1. To find instantaneous velocity on a displacement - time graph, draw a line that is tangent to the curve at that point.
2. The slope is the instantaneous velocity (take the two points on the tangent from each side of the point).
INSTANTANEOUS VELOCITYThis is Jennifer’s trip to school today. Did she have travel with uniform motion at any time on her trip? What are her velocities at times A, B, and C?
In order to determine Jennifer’s velocity we must find the slope at point A, then point B, and C. We draw a tangent line at each point.
A tangent line only touches the curve once.
Point A Two points on the tangent line: ( , ) & ( , )The slope of the tangent is
m = =
Point B Two points on the tangent line: ( , ) & ( , )The slope of the tangent is
m = =
Point C Two points on the tangent line: ( , ) & ( , )The slope of the tangent is
m = =
GRAPHING MOTION Worksheet POSITION-TIME Lab
Interpreting Displacement - Time Graphs in order to constructVelocity Time Graphs
VELOCITY-TIME GRAPHS Worksheet
Physics 11 – Assignment #1
Directions: Show all work for full value. Remember to consider units and significant figures in your answers
1. A cheetah can run with a maximum speed of 110 km/hr. If his sprint lasts 5.0 s, how far does he travel?
2. An orbiting satellite attains a speed of 1500. km/h. How long would it take to travel 2.00 x 105 km?
3. In a game of dodge ball, the ball is hurled with an average velocity of 12.2 m/s at a competitor standing 13.0 m away. If the target has a reaction time of 1.2 seconds, will he get hit by the ball? Prove your answer.
4. You and a friend each drive 50.0 km. You travel at 90.0 km/h, your friend at 95.0 km/hr. How long will your friend wait for you at the end of the trip?
5. You plan a trip on which you want to average 90.0 km/h. You cover the first half of the distance at an average speed of only 48 km/h. What must your average speed be in the second half of the trip to meet your goal? (Hint: average velocity is dependant on time, not distance – this is a difficult question).
6. The position – time graph below indicates the motion of 3 vehicles. Construct a velocity – time graph, and convert the motion of all three vehicles.
Ya
d(m)b
X
c
7. Solve the following question GRAPHICALLY and ALGEBRAICALLY. Car A leaves Dartmouth for Truro (a distance of 100. km) at 70.0 km/h. At the same time, car B leaves Truro for Dartmouth at 100.0 km/h.
a. How far from Dartmouth do they meet? b. At what time from the start?
(Hint: To solve algebraically, determine the linear equation defining the motion of each car, and then set up a system of equations and solve for x and y)
