Accelerated Motion Velocity, acceleration and gravity

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Transcript of Accelerated Motion Velocity, acceleration and gravity

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Accelerated Motion Velocity, acceleration and gravity Slide 2 How fast do things fall Slide 3 Reflexes Slide 4 Position-Time Graphs 1234 Slide 5 Velocity v. Time Slide 6 Definitions Velocity Velocity Change in position with respect to time Change in position with respect to time v = d/t v = d/t Which can be written as: (d final -d initial )/(t final -t initial ) Common notation: (d f d i )/(t f t i ) Acceleration Change in velocity with respect to time a = v/t Which can be written as: (v final -v initial )/(t final -t initial ) Common notation : (v f v i )/(t f t i ) Slide 7 Velocity to Acceleration v=d/t=(d final d initial )/(t final t initial ) v=d/t=(d final d initial )/(t final t initial ) a=v/t=(v final v initial )/(t final t initial ) a=v/t=(v final v initial )/(t final t initial ) Slide 8 Slide 9 Average Acceleration a =v/t=(v final v initial )/(t final t initial ) a =v/t=(v final v initial )/(t final t initial ) f = final f = final i = initial i = initial If t initial = 0 If t initial = 0 a = (v final v initial )/t final a = (v final v initial )/t final Or: Or: v f = v i +at f v f = v i +at f Slide 10 Positive and Negative Acceleration Slide 11 Practice Problem A soccer player is running at a constant velocity of 50.0km/h (31mph). The player falls and skids to a halt in 4.0 seconds. A soccer player is running at a constant velocity of 50.0km/h (31mph). The player falls and skids to a halt in 4.0 seconds. What is the average acceleration of the player during the skid? What is the average acceleration of the player during the skid? What is the plot of the velocity vs. time? What is the plot of the velocity vs. time? Slide 12 Practice Problem A water balloon in the sling of a water balloon launcher undergoes a constant acceleration 25m/s^2 for 1.5s. A water balloon in the sling of a water balloon launcher undergoes a constant acceleration 25m/s^2 for 1.5s. What is the velocity of the water balloon right after launch? What is the velocity of the water balloon right after launch? Slide 13 Practice Problem A car accelerates from rest at 5 m/s2 for 5 seconds. It moves with a constant velocity for some time, and then decelerates at 5 m/s2 to come to rest. The entire journey takes 25 seconds. Plot the velocity-time graph of the motion. A car accelerates from rest at 5 m/s2 for 5 seconds. It moves with a constant velocity for some time, and then decelerates at 5 m/s2 to come to rest. The entire journey takes 25 seconds. Plot the velocity-time graph of the motion. Slide 14 Practice Problem Determine the accelerations for a 1, a 2, a 3, and a 4 for each time interval. a 1 = 4/5 a 2 = (4-4)/(10-5) a 3 = (16-4)/(20-10) a 4 = (0-16)/(30-20) Slide 15 Frictionless Cars Hypotenuse Gravity Slide 16 Frictionless Car Plots Slide 17 Good Reading on Plot Slide 18 Velocity with Constant Acceleration Given: Given: Solve Solve for tf: for tf: Substitute in: Substitute in: Yeilds: Yeilds: 2 2 Slide 19 Velocity with Constant Acceleration Solve for vf Solve for vf 2 2 1 1 2 2 2 1 1 2 2 2 2 2 2 2 2 22 2 2 2 Slide 20 Graphs Determine which equations provide the area under the graph. (let ti = 0) Determine which equations provide the area under the graph. (let ti = 0) (v f -v i ) tftftftf a (t f -t i ) 2 (v f -v i ) (t f -t i ) 2 1 2 Velocity (m/s) Time (s) 1) 2) 3) Slide 21 Velocity with Constant Acceleration Equation to remember: Equation to remember: v f ^2 = v i ^2 +2a(d f -d i ) v f ^2 = v i ^2 +2a(d f -d i ) Slide 22 Position with Average Acceleration d/t = v + a t d/t = v + a t d = vt + a t^2 d = vt + a t^2 When t i = 0: When t i = 0: d f - d i = v i t f + at f ^2 d f - d i = v i t f + at f ^2 Slide 23 Position with Average Acceleration Equation to remember: Equation to remember: Final position = initial position + (change in velocity)*time + (acceleration)*(time squared) Final position = initial position + (change in velocity)*time + (acceleration)*(time squared) d f = d i + (v f -v i )t + at^2 d f = d i + (v f -v i )t + at^2 Slide 24 Table 3-3 Page 68 Equations of Motion for Uniform Acceleration Equations of Motion for Uniform Acceleration Equation Variable s Initial Conditi ons Average Acceleration t f,v f,a vivivivi Velocity with Constant Acceleration t f,d f,a d i,v i Position with Average Acceleration d f,v f, a d i,v i Slide 25 Free Fall on the Moon Slide 26 Slide 27 Group Project pg 78 How fast is the Earth spinning? How fast is the Earth spinning? 0.5 km/sec 0.5 km/sec How fast is the Earth revolving around the Sun? How fast is the Earth revolving around the Sun? 30 km/sec 30 km/sec How fast is the Solar System moving around the Milky Way Galaxy? How fast is the Solar System moving around the Milky Way Galaxy? 250 km/sec 250 km/sec How fast is our Milky Way Galaxy moving in the Local Group of galaxies? How fast is our Milky Way Galaxy moving in the Local Group of galaxies? 370 km/sec 370 km/sec Slide 28 Free Fall All Objects fall at the same speed regardless of mass (if you can neglect wind resistance). All Objects fall at the same speed regardless of mass (if you can neglect wind resistance). Slide 29 Free Fall A ball or a bullet? A ball or a bullet?.. Position with Average Acceleration Height with constant gravity Slide 30 Falling Slide 31 Poor little guy Slide 32 Graphs Slide 33 Cart Movement Slide 34 Practice Problems If you throw a ball straight upward, it will rise into the air and then fall back down toward the ground. If you throw a ball straight upward, it will rise into the air and then fall back down toward the ground. Imagine that you throw the ball with an initial velocity of 10.0 m/s. Imagine that you throw the ball with an initial velocity of 10.0 m/s. a. How long does it take the ball to reach the top of its motion? a. How long does it take the ball to reach the top of its motion? b. How far will the ball rise before it begins to fall? b. How far will the ball rise before it begins to fall? c. What is its average velocity during this period? c. What is its average velocity during this period? Slide 35 a. How long does it take the ball to reach the top of its motion? Slide 36 b. How far will the ball rise before it begins to fall? Slide 37 c. What is its average velocity during this period? Slide 38 Practice Problem A sudden gust of wind increases the velocity of a sailboat relative to the water surface from 3.0 m/s to 5.5 m/s over a period of 60.0 s. A sudden gust of wind increases the velocity of a sailboat relative to the water surface from 3.0 m/s to 5.5 m/s over a period of 60.0 s. a. What is the average acceleration of the sailboat? a. What is the average acceleration of the sailboat? b. How far does the sailboat travel during the period of acceleration? b. How far does the sailboat travel during the period of acceleration? Slide 39 a. What is the average acceleration of the sailboat? Slide 40 b. How far does the sailboat travel during the period of acceleration? Slide 41 Practice Problem A car starts from rest with an acceleration of 4.82 m/s^2 at the instant when a second car moving with a velocity of 44.7 m/s (100mph by the way) passes it in a parallel line. How far does the first car move before it overtakes the second car? A car starts from rest with an acceleration of 4.82 m/s^2 at the instant when a second car moving with a velocity of 44.7 m/s (100mph by the way) passes it in a parallel line. How far does the first car move before it overtakes the second car? Setup an equation or graph Setup an equation or graph Slide 42 Setup the equation 00 Slide 43 Slide 44 Position d Slide 45 Velocity v=d/t Slide 46 Acceleration a=v/t Slide 47 Slide 48