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One-Dimensional Motion

One-Dimensional Motion. Acceleration and Uniformly accelerated motion. One-Dimensional Motion. Acceleration. Objectives. Define acceleration Solve acceleration problems Draw and interpret velocity versus time and acceleration versus time graphs. Acceleration.

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One-Dimensional Motion

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  1. One-Dimensional Motion Acceleration and Uniformly accelerated motion

  2. One-Dimensional Motion Acceleration

  3. Objectives • Define acceleration • Solve acceleration problems • Draw and interpret velocity versus time and acceleration versus time graphs

  4. Acceleration • The speeding up or slowing down of an object • The rate that velocity changes, so the change in velocity over the change in time • a= Δv/Δt= V f – V i/ t f – t I • Units- m/s2 • Vector or scalar?

  5. Instantaneous Versus Average • Average acceleration-change in velocity over an interval of time • Instantaneous Acceleration-change in velocity at an instant of time

  6. Example • A sprinter goes from 10 m/s to 15 m/s in 5 seconds, at what rate is the sprinter accelerating?

  7. Example • I am driving east at 9.0 m/s and I see a deer and stop in 5.0 seconds. What is the acceleration?

  8. Example • A runner starts at a velocity of 1.2 m/s and speeds up constantly during a workout at a rate of 0.2m/s2. After 25 minutes what is the speed of the runner?

  9. Velocity Versus Time Graph • Velocity • Time • Slope=rise over run • What does slope indicate here?

  10. Example • Velocity • Time • What does this tell us about the acceleration?

  11. Example Continued • Accel • time Acceleration is __________ and is below the time axis because _________________

  12. Example Continued • What does the distance versus time graph look like?

  13. Example • Velocity • Time • Draw the acceleration vs time graph and the position vs time

  14. Example Continued A-T graph

  15. Example Continued- D-T graph

  16. Review • Position Versus Time graph • Slope=velocity • +slope=movement to the right/up • -slope=movement to the left/down • Linear=constant velocity, no acceleration

  17. Review • Velocity Versus Time Graph • Slope=acceleration • +slope=speeding up • -slope=slowing down • Slope DOES NOT indicate direction here • Slope of 0=no acceleration • If the line is above the time axis the object is moving to the right • If the line is below the time axis the object is moving to the left • Straight line=constant accleration

  18. Review • Acceleration Versus Time Graph • Straight horizontal line=constant acceleration • Below the X axis=slowing down • Above the X axis=speeding up

  19. One-Dimensional Motion Uniformly Accelerated Motion

  20. Objectives • Solve problems using uniform acceleration equations

  21. Uniformly Accelerated Motion • Acceleration is constant • What would a velocity versus time graph look like with constant acceleration? Without constant? • Equations • V f = V i+ at • Δx = V iΔt + ½ (a t2) • Vf2 = Vi2 + 2 a Δx • Δx = ½ (Vf + Vi) Δt • What variables do we have?

  22. Example • How long must a runway be for a plane to reach a takeoff velocity of 75 m/s if it accelerates at 20 m/s2?

  23. Example • My tea tumbler falls off my car and slides along 95 South for 75 m. Friction slows my tumbler at 6 m/s2. • A)How fast was the car moving when the tumbler fell? • B)How long did it take the tumbler to stop?

  24. Example A police car chases after a robber who is moving at 50 m/s East. If the police car starts out going 5 m/s east, and accelerates at 8 m/s2 east for 6 seconds. What will be the velocity of the police car after 3 seconds? How far will the police car travel? How far will the robber travel in the same time if he does not accelerate?

  25. One-Dimensional Motion Freefall

  26. Objectives • Define freefall • Solve freefall problems

  27. Freefall • If the only force acting upon an object is gravity the object is said to be in freefall • No _________________ • Considered to be uniform accelerated motion • g is the acceleration due to gravity= 9.8 m/s2 • When an object is in freefall we will use -9/8 m/s2 • Does mass matter? • What would a distance versus time graph look like for a ball being thrown in the air?

  28. Example • A ball is dropped from a height of 2.0 m. What is the velocity before it strikes the ground? How long did it take to hit the ground?

  29. Example Cont • Draw the position, velocity, and acceleration graphs

  30. Example continued • How long would it take for the same ball to be thrown up 2m and then fall to the ground?

  31. Example • A ball is thrown straight down with a speed of 0.50 m/s from a height of 4.0 m. What is the speed of the ball 0.70 seconds after the ball is released?

  32. Example • A 0.25 kg baseball is thrown upward w/ a speed of 30 m/s. Neglect friction. What is the maximum height that the baseball reaches?

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