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## Catalyst

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**Catalyst**• 1. What is the acceleration of an ant that begins crawling at 2 m/hr and speeds up to 3 m/hr in 1 hour? (Use the acceleration equation.) • 2. For a car that can go from 0 m/s to 100 m/s in 25 seconds, what would its final velocity be if it started from rest and accelerated for 10 seconds?**Setting Up Your Graph**• Position vs. Time Graphs • Distance on the vertical axis • Time on the horizontal axis • Label each axis • Make a scale for each axis**Analyzing Graphs**• The slope of a graph is equal to rise/run which is equal to distance/time… the slope tells you your speed! • We can analyze graphs to get the instantaneous speed at certain intervals.**Position vs. Time Graphs**• What can we get from this graph?**Position vs. Time Graph Demonstration**• http://zonalandeducation.com/mstm/physics/mechanics/kinematics/xvaVsTime/xVsTime.html**Position vs. Time Graphs**1. Total displacement How? Find the starting position in meters, find the ending position in meters, and take the difference**Position vs. Time Graphs**2. Distance traveled during any time interval How? Pick your time interval, find the starting position in meters, find the ending position in meters, and take the difference**Position vs. Time Graphs**3. Total distance traveled How? Find the distance for all the line segments, then add**Position vs. Time Graphs**4. Time spent motionless How? Find all of the horizontal line segments (where slope is 0), find their lengths in seconds, then add**Position vs. Time Graphs**5. Instantaneous speed during any time interval How? Find the slope of the line segment using change in distance/change in time Steeper slope = greater speed**Motion Graphs**• There are THREE types: • Position vs. Time • Gives your position over a period of time. • Velocity vs. Time • Gives your speed (velocity) over a period of time. • Acceleration vs. Time • Gives your acceleration over a period of time.**Velocity vs. Time Graphs**• These are new! • Slope is acceleration • Straight lines mean constant acceleration**Velocity vs. Time Graphs**• Curved lines mean changingacceleration • Cannot find slope of curved lines**Velocity vs. Time Graphs**• Horizontal (flat) lines mean no acceleration or constant speed**Velocity vs. Time Graph Demonstration**• http://www.physicsclassroom.com/mmedia/kinema/fs.cfm**Acceleration vs. Time Graphs**• Flat lines mean constant acceleration • Everything else means nothing! (for our purposes) • The only other acceleration vs. time graph you will see is this: • Which means no acceleration**Example: No Motion**Position vs. Time Velocity vs. Time Acceleration vs. Time**Example: Constant Velocity**Position vs. Time Velocity vs. Time Acceleration vs. Time**Example: Constant Acceleration = Object is Speeding Up**Position vs. Time Velocity vs. Time Acceleration vs. Time**Example**+ = ? B A**Example**A B Use the tip-to-tail method to add your vectors. This means the tip (or head) of one vector (vector A) arrow meets the tail of the other vector arrow (vector B)**Example**A B C Use the tip-to-tail method to add your vectors. Your resultant is the vector arrow that goes from the tail of A to the tip of B. Your resultant can be called Vector C.**Example**+ = ? B A**Example**B A Use the tip-to-tail method to add your vectors. This means the tip (or head) of one vector (vector A) arrow meets the tail of the other vector arrow (vector B)**Example**B A Use the tip-to-tail method to add your vectors. Your resultant is the vector arrow that goes from the tail of A to the tip of B. Your resultant can be called Vector C. Pythagorean Theorem!**Practice**To complete the following problems, draw the vectors first and then add them to find the resultant and answer the problem. Add the velocities 15 m/s north + 6 m/s east. Add the velocities 10 m/s north + 5 m/s south. Find the resultant displacement if an ant walks 12 cm north and 8 cm west. Find the total velocity if Ricky runs 5 m/s east along a conveyor belt moving at 2 m/s east.**More Kinematic Equations**One example… • A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.5 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?