1 What is Physics? Motion in One Direction

2 What is Physics? The study of how stuff works The study of how stuff works Deals with the behavior of matter Deals with the behavior of matter Fundamental science (quantitative) Fundamental science (quantitative) Uses mathematics as a compact language to explain various concepts Uses mathematics as a compact language to explain various concepts Major subfields: Major subfields: - classical physics: mechanics; thermodynamics; electricity & magnetism; optics - classical physics: mechanics; thermodynamics; electricity & magnetism; optics - modern physics: atomic physics; nuclear physics; particle physics; condensed-matter physics

3 Frames of Reference Vantage point with respect to which position and motion may be described Vantage point with respect to which position and motion may be described Ex: Imagine you are on a train that is stopped at the platform. You walk toward the front of the train at 3 m/s. To everyone on the train & platform you appear to move at 3 m/s. Ex: Imagine you are on a train that is stopped at the platform. You walk toward the front of the train at 3 m/s. To everyone on the train & platform you appear to move at 3 m/s. Now the train has begun to move past the platform at 9 m/s. Everyone on the train will agree that you are still moving at 3 m/s BUT to people on the platform it appears that you are moving at 12 m/s. Now the train has begun to move past the platform at 9 m/s. Everyone on the train will agree that you are still moving at 3 m/s BUT to people on the platform it appears that you are moving at 12 m/s.

4 Average and Instantaneous Speed Average speed is the distance an object travels divided by the time it takes. Average speed is the distance an object travels divided by the time it takes. Constant speed means the same distance is traveled every second. Constant speed means the same distance is traveled every second. Instantaneous speed is the speed you are going NOW Instantaneous speed is the speed you are going NOW Speed is a ratio of distance over time so the standard units for speed are meters per second Speed is a ratio of distance over time so the standard units for speed are meters per second

5 Formula for Speed Average speed = distance traveled/time of travel Average speed = distance traveled/time of travel OR OR s = d/t s = d/t s = speed d = distance t = time s = speed d = distance t = time

6 Practice: Speed An airplane flies 450 meters in 3 seconds. What is its speed in meters per second? An airplane flies 450 meters in 3 seconds. What is its speed in meters per second? A train is moving at a speed of 50 kilometers per hour. How many hours will it take the train to travel 600 kilometers? Convert your answer to meters per second. A train is moving at a speed of 50 kilometers per hour. How many hours will it take the train to travel 600 kilometers? Convert your answer to meters per second. A boy runs at a speed of 3 meters per second for 60 seconds. How far did he run? A boy runs at a speed of 3 meters per second for 60 seconds. How far did he run?

7 Velocity Speed plus direction Speed plus direction v is the symbol for velocity v is the symbol for velocity Average velocity = displacement of object/time Average velocity = displacement of object/time OR OR v = d/t v = d/t V = velocity d = displacement t = time V = velocity d = displacement t = time Displacement = distance between stopping and starting position of an object in motion Displacement = distance between stopping and starting position of an object in motion

8 Instantaneous Velocity Equal to the instantaneous speed plus the direction the object is moving in at that instant Equal to the instantaneous speed plus the direction the object is moving in at that instant Changes in instantaneous velocity require the intervention of force Changes in instantaneous velocity require the intervention of force Changes in velocity can be a change in speed OR a change in direction OR both Changes in velocity can be a change in speed OR a change in direction OR both

9 Scalar & Vector Quantities Scalars are quantities which are fully described by a magnitude alone. Scalars are quantities which are fully described by a magnitude alone. Vectors are quantities which are fully described by both magnitude and a direction. Vectors are quantities which are fully described by both magnitude and a direction.

10 Examples: Scalar & Vector Speed is a scalar quantity which refers to how fast an object is moving. Speed has only magnitude Speed is a scalar quantity which refers to how fast an object is moving. Speed has only magnitude Velocity is a vector quantity which refers to the rate at which an object changes its position. Velocity has both magnitude and direction Velocity is a vector quantity which refers to the rate at which an object changes its position. Velocity has both magnitude and direction

11 More Examples; Scalar & Vector Distance is a scalar quantity which refers to the total distance an object has covered during its motion. Distance is a scalar quantity which refers to the total distance an object has covered during its motion. Displacement is a vector quantity which refers to the distance an object moved from its original position. Displacement is a vector quantity which refers to the distance an object moved from its original position.

12 Practice: Scalar vs. Vector Identify the following quantities as scalar or vector: Identify the following quantities as scalar or vector:   5 m   30 m/sec, East   30 m/sec   5 mi., North   20 degrees Celsius   256 bytes   4000 calories

13 More Practice: Distance vs. Displacement A physics student walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. What is the distance traveled? What is the student’s displacement?

14 The skier moves from A to B to C to D. Determine the resulting displacement and distance traveled by the skier during the three minutes

15 Acceleration the rate at which an object’s motion changes – it can be an increase or decrease in speed and/or a change in direction the rate at which an object’s motion changes – it can be an increase or decrease in speed and/or a change in direction Acceleration is measured in meters/second/second or m/s 2 Acceleration is measured in meters/second/second or m/s 2 Average acceleration is calculated: Average acceleration is calculated: A = v 2 – v 1 / t a = acceleration v 2 = final velocity v 1 = initial velocity t = time v 1 = initial velocity t = time

16 Instantaneous Acceleration Rate at which velocity is changing in a given instant of time Rate at which velocity is changing in a given instant of time Calculated by finding the average acceleration for a very short time interval during which acceleration does not change appreciably Calculated by finding the average acceleration for a very short time interval during which acceleration does not change appreciably

17 Direction of Acceleration Acceleration is a vector quantity Acceleration is a vector quantity Direction of acceleration vector is that of the change in velocity Direction of acceleration vector is that of the change in velocity If velocity is increasing, acceleration is in the same direction as velocity itself If velocity is increasing, acceleration is in the same direction as velocity itself If velocity is decreasing, acceleration is in the opposite direction (resulting in a negative acceleration) If velocity is decreasing, acceleration is in the opposite direction (resulting in a negative acceleration)

18 Practice: Acceleration A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 seconds. What is the boat’s acceleration? A sailboat moves at 1 m/s. A strong wind increases its speed to 4 m/s in 3 seconds. What is the boat’s acceleration? Calculate the acceleration of an airplane that starts at rest and reaches a speed of 45 m/s in 9 seconds. Calculate the acceleration of an airplane that starts at rest and reaches a speed of 45 m/s in 9 seconds. The driver of a car steps on the brakes, and velocity drops from 25 m/s due east to 15 m/s due east in a time of 2.0 seconds. What is the acceleration? The driver of a car steps on the brakes, and velocity drops from 25 m/s due east to 15 m/s due east in a time of 2.0 seconds. What is the acceleration?

19 Graphing Motion Motion graphs show the relationships between distance, speed, acceleration, and time Motion graphs show the relationships between distance, speed, acceleration, and time Two main types of graphs of motion are: Two main types of graphs of motion are: - distance vs. time - distance vs. time - velocity (speed) vs. time - velocity (speed) vs. time

20 Distance vs. Time Graph Distance is plotted on the y-axis & time is plotted on the x-axis Distance is plotted on the y-axis & time is plotted on the x-axis This distance-time graph illustrates constant speed – motion of an object

position vs time worksheet Calculations: Dist. vs. Time Graph To calculate speed you need to find the slope: To calculate speed you need to find the slope: Slope equals rise/run Slope equals rise/run Rise is the vertical change Rise is the vertical change Run is the horizontal change Run is the horizontal change Since the y axis measures distance and the x axis measures time we get the formula speed = distance/time Since the y axis measures distance and the x axis measures time we get the formula speed = distance/time

22 Speed vs. Time Graph (constant speed) The speed vs. time graph has speed on the y axis and time on the x axis The speed vs. time graph has speed on the y axis and time on the x axis Constant speed is shown with a straight horizontal line. Constant speed is shown with a straight horizontal line.

23 Speed vs. Time Graphs Positive acceleration Negative acceleration Positive acceleration Negative acceleration No acceleration

24 Calculating Acceleration: Speed vs Time Graph Instantaneous acceleration is equal to the slope Instantaneous acceleration is equal to the slope A steep slope equals a rapid change in velocity (large acceleration) A steep slope equals a rapid change in velocity (large acceleration) A horizontal line equals no change in velocity (no acceleration) A horizontal line equals no change in velocity (no acceleration) A gradual slope equals a slow change in velocity (small acceleration) A gradual slope equals a slow change in velocity (small acceleration)

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26 Calculating Distance: Speed vs Time Graph (Constant Speed) A speed vs. time graph can be used to calculate the distance an object has traveled A speed vs. time graph can be used to calculate the distance an object has traveled Remember, distance = speed x time Remember, distance = speed x time Draw a rectangle between the x axis and the line showing speed Draw a rectangle between the x axis and the line showing speed The area of the rectangle is equal to its length x its height – this is the distance the object traveled The area of the rectangle is equal to its length x its height – this is the distance the object traveled

27 Calculating Distance: Speed vs Time Graph (Accelerating Object) Draw a line from the uppermost speed coordinate, creating a triangle Draw a line from the uppermost speed coordinate, creating a triangle Area of a triangle = ½ length x height Area of a triangle = ½ length x height

28 Uniform Acceleration Acceleration does not change as the motion proceeds (maintains the same value at any time) Acceleration does not change as the motion proceeds (maintains the same value at any time)

29 Uniform Acceleration: Velocity vs. Time Graph Positive acceleration will have a constant upward slope (velocity increases at a steady rate) Positive acceleration will have a constant upward slope (velocity increases at a steady rate) Represented by the formula: Represented by the formula: v = v o + at v = v o + at v = velocity v o = original velocity at = change in velocity due to acceleration v = velocity v o = original velocity at = change in velocity due to acceleration Negative acceleration will have a constant downward slope (velocity decreases at a steady rate) Negative acceleration will have a constant downward slope (velocity decreases at a steady rate)

30 Practice: Uniform Acceleration A car traveling due east with an initial velocity of 5 m/s accelerates for 5 seconds at a constant rate of 2 m/s 2. What is its velocity at the end of this time? A car traveling due east with an initial velocity of 5 m/s accelerates for 5 seconds at a constant rate of 2 m/s 2. What is its velocity at the end of this time? The same car then slows down at a rate of 3 m/s 2 over a time of 2 seconds. What is its velocity now? The same car then slows down at a rate of 3 m/s 2 over a time of 2 seconds. What is its velocity now?

31 Uniform Acceleration & Distance When velocity increases at a steady rate, the distance covered grows more & more rapidly When velocity increases at a steady rate, the distance covered grows more & more rapidly When velocity decreases at a steady rate, the distance covered shrinks more & more rapidly When velocity decreases at a steady rate, the distance covered shrinks more & more rapidly Find distance by multiplying the (average) velocity x time Find distance by multiplying the (average) velocity x time Represented by the formula: Represented by the formula: d = v o t + 1/2at 2 d = v o t + 1/2at 2

32 Practice: Uniform Acceleration & Distance A car traveling due east with an initial velocity of 5 m/s accelerates for 5 seconds at a constant rate of 2 m/s 2. How far does it travel during this time? A car traveling due east with an initial velocity of 5 m/s accelerates for 5 seconds at a constant rate of 2 m/s 2. How far does it travel during this time? If the above car begins to slow down at a rate of 3 m/s 2, what stopping distance will be needed to bring the car to a complete stop within 10 seconds? If the above car begins to slow down at a rate of 3 m/s 2, what stopping distance will be needed to bring the car to a complete stop within 10 seconds?