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Accelerated Motion. Velocity, acceleration and gravity. How fast do things fall. Reflexes. Position-Time Graphs. 1. 2. 3. 4. Velocity v. Time. Velocity Change in position with respect to time v = Δ d/ Δ t Which can be written as: (d final -d initial )/(t final -t initial )

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## Accelerated Motion

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**Accelerated Motion**Velocity, acceleration and gravity**Position-Time Graphs**1 2 3 4**Velocity**Change in position with respect to time v = Δd/Δt Which can be written as: (dfinal-dinitial)/(tfinal-tinitial) Common notation: (df–di)/(tf–ti) Acceleration Change in velocity with respect to time a = Δv/Δt Which can be written as: (vfinal-vinitial)/(tfinal-tinitial) Common notation : (vf–vi)/(tf–ti) Definitions**Velocity to Acceleration**• v=Δd/Δt=(dfinal–dinitial)/(tfinal–tinitial) • a=Δv/Δt=(vfinal–vinitial)/(tfinal–tinitial)**Average Acceleration**• a =Δv/Δt=(vfinal–vinitial)/(tfinal–tinitial) • f= final • i = initial • If tinitial = 0 • a = (vfinal – vinitial)/tfinal • Or: • vf = vi +atf**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. • What is the average acceleration of the player during the skid? • What is the plot of the velocity vs. time?**Practice Problem**• 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?**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.**Practice Problem**Determine the accelerations for a1, a2, a3, and a4 for each time interval. a1= 4/5 a2= (4-4)/(10-5) a3= (16-4)/(20-10) a4= (0-16)/(30-20)**Gravity**Hypotenuse Frictionless Cars**2**½ 2 ½ Velocity with Constant Acceleration • Given: • Solve • for tf: • Substitute in: • Yeilds:**Velocity with Constant Acceleration**• Solve for vf 2 ½ 2 1 1 ½ 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2**Graphs**• Determine which equations provide the area under the graph. (let ti = 0) (vf-vi) (tf-ti) ½ 1) Velocity (m/s) 2) 2 a tf ½ 3) (vf-vi) 2 1 (tf-ti) 2 (tf-ti) Time (s)**Velocity with Constant Acceleration**• Equation to remember: • vf^2 = vi^2 +2a(df-di)**Position with Average Acceleration**• Δd/Δt = Δv + ½ a Δt • Δd = ΔvΔt + ½ a Δt^2 • When ti = 0: • df - di = vitf + ½ atf^2**Position with Average Acceleration**• Equation to remember: • Final position = initial position + (change in velocity)*time + ½ (acceleration)*(time squared) • df = di + (vf-vi)t + ½ at^2**Table 3-3 Page 68**• Equations of Motion for Uniform Acceleration**Group Project pg 78**• How fast is the Earth spinning? • 0.5 km/sec • How fast is the Earth revolving around the Sun? • 30 km/sec • How fast is the Solar System moving around the Milky Way Galaxy? • 250 km/sec • How fast is our Milky Way Galaxy moving in the Local Group of galaxies? • 370 km/sec**Free Fall**• All Objects fall at the same speed regardless of mass (if you can neglect wind resistance).**Free Fall**• A ball or a bullet? • . • . Position with Average Acceleration Height with constant gravity**Practice Problems**• 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. • 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? • c. What is its average velocity during this period?**a. How long does it take the ball to reach the top of its**motion?**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. 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?**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? • Setup an equation or graph

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