1. 1 Dimensional Motion

2. What you learned from you lab… Objects moving at constant velocityObjects accelerating

3. Position, Distance, & Displacement Acknowledge your origin. Remember it might not be where you are actually starting Position is where you are at an instant in time Distance is a scaler quantity and measures your total movement Displacement is a vector quantity that measures the straight line distance between the starting position and the ending positon. This must have a magnitude and direction The distance an objects travels is always ________________________ to its displacement Greater than or equal to

4. Below is the map of a person’s walk to school What is the total distance the person traveled? What is the magnitude and direction of the person’s displacement? If the person walked back home after school following the route in reverse, what is the total distance traveled? What is the magnitude and direction of the person’s total displacement? 800m East in 5 minutes 400m North in 3 minutes 350m East in 2 minutes Wait for your friend for 2.5 minutes

5. Speed & Average Speed Speed is a scalar quantity that measures how fast you are moving. It is calculated using values that represent DISTANCE. Your average speed is calculated by taking your total distance and dividing it by the total time it took to travel that distance. Stopping time is included in this calculation 1. If you travel 100 km at 20km/hr then travel 100km at 50km/hr, what is your overall average speed? Can you take the average of the two speeds? 2. If you travel for 5 hours at 20km/hr then travel for 5 hours at 60km/hr, what is your overall average speed? Can you take the average of the two speeds? 28.6 km/hr 40.0 km/hr Is there a rule about calculating average speed?

6. Velocity, Average Velocity, & Instantaneous Velocity Velocity is a vector quantity describing how fast you are moving. It is calculated using the value for DISPLACEMENT Your average velocity is calculated by taking your total displacement and dividing it by the total time it took to travel that displacement. Stopping time is included in this calculation Your instantaneous velocity is your velocity at one instant in time. 1.Your average speed will always be __________________________ your average velocity. 2.Can your instantaneous velocity be zero while your average velocity is not? Explain. Greater than or equal to Yes, when you turn around, you stop for a second but still are moving overall

7. Below is the map of a person’s walk to school What is the average speed of the person? What is the magnitude and direction of the person’s velocity? If the person walked back home after school following the route in reverse, but without stopping, what is the person’s average speed ON THE WAY HOME? What is the magnitude and direction of the person’s average velocity for the entire day? 800m East in 5 minutes 400m North in 3 minutes 350m East in 2 minutes Wait for your friend for 2.5 minutes 124m/min 97.4m/min @ 19.2 o N of E 155m/min 0 m/min

8. Below is the position (m) vs. time (s) graph for an object moving left and right. (right is considered the positive direction) 1.What is the overall average speed of the object? 2.What is the object’s total average velocity? 3.How would you determine the instantaneous velocity of this object? 4.When is the instantaneous velocity of the object the greatest? 5.When is the instantaneous velocity zero? A B C D 10m -7m 5 10 15 20 1.2m/s -0.5m/s Find the slope of the tangent line Point B A and C

9. Acceleration The rate at which velocity is changing If the acceleration and velocity vectors are in the same direction, the object is speeding up. If the acceleration and velocity vectors are in the opposite direction, the object is slowing down. 1.Can an object be accelerating when its instantaneous velocity is zero? 2.Can an object be accelerating when its speed is constant? Yes, when its turning around Yes, when its moving in a circle

10. Free Fall - Dropped An object in the air under the influence of Gravity only. (air resistance is usually neglected) On Earth, the acceleration of an object in free fall is always 9.81m/s 2 downwards throughout the entirety of the motion. In this case it might be helpful to make the downward direction positive so all your calculations do not end up with negative signs “dropped” implies v o is zero m/s All three acceleration formulas are valid. CAN NOT USE THE CONSTANT SPEED FORMULA FOR FREE FALL!

11. Thrown Downwards The object’s velocity will increase as it falls The initial velocity will be downwards (you can choose that to be positive for ease) The acceleration is still 9.81m/s 2 downwards v t

12. Thrown Upwards The initial velocity will be a positive value The acceleration must be negative The instantaneous velocity at the top of the motion is 0m/s The final velocity will be negative if its on the way down. The displacement is zero if the object is caught at the same height it is thrown from. At this point, the magnitude of the downward velocity is equal in magnitude to the initial upwards velocity. At any point below the initial release point, the magnitude of the object’s velocity is greater than its initial velocity. The displacement is positive if the object is lands at a point higher than its release The displacement is negative if the object is lands at a position lower than it was thrown from. v t

13. Two objects Dropped Simultaneously Both have the same initial velocity Both have the same downward acceleration -------------------------------------------------------------------------------- They must be moving at the same instantaneous velocity at any point. They must have the same displacement at any given time. They will take the same amount of time to hit the floor. The mass of the object does NOT affect its acceleration due to gravity!

14. Practice 1.An object is dropped from a bridge 20m high a.How long does it take to hit the water below? b.What is its velocity when it hits the water? 2.An object is thrown downwards off of a cliff at 7m/s. If the object hits the ground 3 seconds later a.How high is the cliff? b.How fast is it moving when it hits the ground? 3.A coin is thrown upwards at 4.5m/s during a coin toss. If the coin is caught at the same height it was released from, a.What is the max height above the release point of the coin? b.How long is it in the air for? c.What is the coin’s velocity when it is caught? 4.A water balloon is thrown down from a window 12m above the ground. If the water balloon hits the ground moving at 20m/s, a.How fast was it thrown out of the window? b.Was it thrown up or down? EXPLAIN c.How long was it in the air for? 2 seconds 19.8m/s 65.1m 36m/s 1.03m 0.92s 4.5m/s downwards 12.8m/s It can be thrown up or down because it reaches that same speed on the way down. 0.7 seconds

16. Two objects Dropped 1.0 Second Apart d A (m)v A (m/s) Time A (s) Time B (s) d B (m)v B (m/s) 1 21 32 43 54 Calculate the instantaneous velocity and the displacement of the object after each interval of time. 1.What do you notice about the difference in velocity of A and B for each row? 2.What to you notice about their difference in positon for each row. 9.81 19.6 29.4 39.2 49.1 9.81 19.6 29.4 39.2 4.9 19.6 44.1 78.5 122.6 4.9 19.6 44.1 78.5 It’s the same difference every time Each second the objects are farther apart

17. Position vs. Time Graphs Y- value is the initial position Above x-axis is positive position Below x-axis is negative position Slope is velocity Positive slope is moving in the positive direction Negative slope is moving in the negative direction Horizontal line = standing still Diagonal line = constant speed Increasing slope = speeding up Decreasing slope = slowing down

18. Velocity vs. Time Graphs Y- value is the instantaneous velocity Above x-axis is moving in the positive direction Below x-axis is moving in the negative direction Slope is acceleration Area is displacement Decreasing the magnitude of y-value means slowing down Increasing the magnitude of y-value means speeding up Horizontal line = constant speed Diagonal line = accelerating Line on x-axis = standing still

19. Acceleration vs. Time Graphs Y- value is the instantaneous acceleration Above x-axis is accelerating in the positive direction Below x-axis is accelerating in the negative direction Area is change in velocity Horizontal line = constant acceleration Diagonal line =changing accelerating Line on x-axis = constant velocity

20. Two Stage Motion 1.A racecar accelerates from rest for 5 seconds at a rate of 7m/s 2 then continues at a constant speed for an additional 20 seconds. How long is the race? 2.A child on a bicycle rides 300m at a constant speed of 7m/s then begins to slows to a stop at a rate of 0.53m/s 2. a.How long does this take? b.How far does the kid ride total 3.A drive to a friend’s house takes 5 minutes. For the first 15 second, the car accelerates out of the driveway and covers 130 meters. The car maintains that constant speed of 4 minutes until it begins to slow to a stop in the remaining time. How far away is your friend’s house? 787.5m 56.1 seconds 346.2m 4679.25 m

22. Two Object Motion 1.Two objects are dropped from a building 55m tall. They are dropped 2 seconds apart. a.How much time lapses between when they land? b.How fast is the second moving when the first hits the floor? c.How far above the ground is the second when the first hits the floor? 2.Two objects are thrown from a window 18m high. The red one is thrown up at 10m/s while the blue one is thrown downwards at 10m/s. a.Which object is moving faster when they hit the ground below? b.How much time lapses between when they land? 2 seconds 13.2m/s 46 m Same speed 1.7 seconds

24. Two Object Motion 1.A cop sitting at rest on the side of the road sees a corvette speed by at a constant 63m/s. The moment the corvette passes the cop, he starts to accelerate at a uniform 1.3m/s 2 a.How long does it take the cop to catch the corvette? b.How far down the highway did he go? 96.6 seconds 6106m