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Acceleration and Free Fall

Acceleration and Free Fall. Chapter 2.2 and 2.3. What is acceleration? . Acceleration measures the rate of change in velocity. Average acceleration = change in velocity/ time required for change. Units for acceleration . Sign is very important!. Acceleration has both direction and magnitude

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Acceleration and Free Fall

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  1. Acceleration and Free Fall Chapter 2.2 and 2.3

  2. What is acceleration? • Acceleration measures the rate of change in velocity. • Average acceleration = change in velocity/ time required for change

  3. Units for acceleration

  4. Sign is very important! • Acceleration has both direction and magnitude • A negative value for acceleration does not always mean an object is decelerating!!

  5. 2-4 Acceleration Increasing speed and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration: Speeding up, moving to the right Slowing down, moving to the right Slowing down, moving to the left Speeding up, moving to the left

  6. Fill in the Chart

  7. Graph of Velocity vs Time Question: What does the slope of this graph give you? Answer: ACCELERATION Rise = Δv Run Δt Vf – VAVG = Δv tf – ti = Δt

  8. The Kinematic Equations • You are going to loooooove these! 

  9. Motion with constant acceleration • Kinematic Equations • The relationships between displacement, velocity and constant acceleration are expressed by equations that apply to any object moving with constant acceleration.

  10. Displacement with constant acceleration • Δx = displacement • Vi = initial velocity • Vf = final velocity • Δt = time interval

  11. Example: #1 p.53 in book • A car accelerates uniformly from rest to a speed of 23.7 km/h in 6.5 s. Find the distance the car travels during this time. • Δx = displacement= distance= ? • Vi = initial velocity = rest = 0 km/h • Vf = final velocity = 23.7 km/h • Δt = time interval = 6.5 s Look at final velocity…convert to m/s!!!

  12. Problem Solving • Final velocity conversion • Plug in values and solve for Δx

  13. Velocity with constant uniform acceleration Vf = final velocity Vi = initial velocity a = acceleration Δt = time interval

  14. Example: #2 p.55 • An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s2. Find the final speed after 5.0 seconds. Vf = final velocity=? Vi = initial velocity = 4.3 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s

  15. Solve • Plug in values and solve for Vf Vf= 19 m/s

  16. Displacement with constant uniform acceleration Δx = displacement Vi = initial velocity a = acceleration Δt = time interval

  17. Example: #2 p.55 • An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.0 m/s2. Find the displacement after 5.0 seconds. Δx = displacement=?? Vi = initial velocity= 4.30 m/s a = acceleration= 3.0 m/s^2 Δt = time interval= 5.0 s

  18. Solve! • Plug in values and solve for displacement

  19. Final Velocity after any displacement Vf = final velocity Vi = initial velocity a = acceleration Δx = displacement

  20. Example: p.58 #3 • A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s^2. What is the speed of the car after it has traveled 55 m? • Vf = final velocity=?? • Vi = initial velocity= rest= 0 m/s • a = acceleration= 2.3 m/s^2 • Δx = displacement= 55 m

  21. Solve

  22. Rearranging • Your problems won’t always be so straightforward…make sure to rearrange your equations to solve for the unknown before plugging in your numbers (with units!)

  23. Section 2-3 Falling Objects • Free Fall: Neglecting air resistance, all objects fall with the same constant acceleration

  24. Acceleration due to gravity

  25. Free Fall Acceleration • However, acceleration is a vector. • Gravity acts toward the earth (down) • Therefore, the acceleration of objects in free fall near the surface of the earth is

  26. What we see because of air resistance…

  27. Object falling from rest

  28. Path of a projectile At top of path v= 0 m/s a = -9.81 m/s2

  29. Free Fall Acceleration • At the highest point of an arc, an object has velocity = 0 m/s, acceleration is still -9.81 m/s2 • An object thrown into the air is a freely falling body with

  30. Free Fall Problem p.64 #2 • A flowerpot falls from a windowsill 25.0 m above the sidewalk • A. How fast is the flowerpot moving when it strikes the ground? • B. How much time does a paserby on the sidewalk below have to move out of the way before the flowerpot hits the ground?

  31. Part. A. • What are we looking for: Vf • What do we know? • Displacement: -25 m • Acceleration: -9.81 m/s2 • Vi=0 m/s What equation should we use??

  32. Solve the problem 

  33. Part b. • How much time before the flowerpot hits the ground? • What do we know? • Displacement= -25.0 m • Acceleration = -9.81 m/s2 • V initial= 0 • V final = -22.1 m/s • What are we looking for: Time! • Which equation should we use??

  34. Solve the Problem 

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