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Understanding Acceleration and Free Fall: The Basics of Velocity Change

This article explores the concept of acceleration, defined as the rate at which an object's velocity changes over time. You’ll learn how to calculate acceleration from changes in speed and direction, illustrated with examples like a car accelerating or braking. Additionally, it delves into free fall, gravitational acceleration, and the principles established by Galileo on motion. The impact of air resistance and the concept of terminal velocity are also discussed, highlighting how they affect falling objects.

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Understanding Acceleration and Free Fall: The Basics of Velocity Change

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  1. Acceleration

  2. Change in Velocity • Each time you take a step you are changing the velocity of your body. • You are probably most familiar with the velocity changes of a moving bus or car. • The rate at which velocity (speed or direction) changes occur is called acceleration.

  3. Acceleration= final velocity- starting velocity time Change in velocity = final – starting velocity velocity Acceleration= change in velocity time

  4. A car traveling at 60 mph accelerates to 90 mph in 3 seconds. What is the car’s acceleration? Velocity(final) - Velocity(original) = Acceleration time 90 mph - 60 mph = 3 seconds 30 mph = 3 seconds = 10 mph/second

  5. Positive acceleration Negative acceleration

  6. A car traveling at 60 mph slams on the breaks to avoid hitting a deer. The car comes to a safe stop 6 seconds after applying the breaks. What is the car’s acceleration? Velocity(final) - Velocity(original) = Acceleration time 0 mph - 60 mph = 6 seconds - 60 mph = 6 seconds = - 10 miles per hour per second

  7. - A constant acceleration produces a straight line or linear slope (rise/run). - The slope of a non-linear velocity-time graph (rise/run) will predict an objects instantaneous acceleration. a = v/t

  8. Free fall • The constant acceleration of an object moving only under the force of gravity is "g". • The acceleration caused by gravity is 10 m/s2 • If there was no air, all objects would fall at the same speed • Doesn’t depend on mass • After 1 second falling at 10 m/s • After 2 seconds 20 m/s • 3 seconds 30 m/s

  9. Galileo • 1600’s • Studied how things fell • Didn’t have a good clock • Rolled balls down an inclined plane • Found that the speed increased as it rolled down the ramp

  10. t = 0 t = 1 second t = 2 seconds t = 3 seconds Galileo Acceleration= change in velocity time

  11. Galileo • Same things happen when things fall • Didn’t drop things from Tower of Pisa

  12. v2final = 2gdy • A final velocity can be calculated over a vertical displacement “dy" during free fall using the equation:

  13. dy = 1/2 gt2 • The vertical displacement “dy" that occurs during a specific time of free fall can be determined using the equation: • Or a time interval can also be determined over a specified distance of freefall using the equation: t2 = 2dy /g

  14. Falling • Air resistance will increase as it falls faster • An upward force on the object • Eventually gravity will balance with air resistance • Reaches terminal velocity - highest speed reached by a falling object.

  15. Terminal velocity • Force of gravity is constant • air resistance increases as you speed up • until the force is equal • Equal forces, no acceleration • constant velocity terminal velocity

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