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Acceleration: Exploring the Rate of Change in Velocity

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Learn about acceleration, the rate of change in velocity, with formulas, symbol, units, and demonstrations. Discover how force impacts velocity changes and solve acceleration word problems.

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Acceleration: Exploring the Rate of Change in Velocity

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  1. Acceleration The last topic in Physics!

  2. Reminder • If you see this on a POSITION-TIME graph: • It means that the object is moving with UNIFORM MOTION • If you see this on a POSITION-TIME graph: • It means that the object has a CHANGE in VELOCITY

  3. Reminder • A CHANGE in VELOCITY means that the object has either: • Changed speed (faster or slower) • Changed direction • Both

  4. Acceleration • Acceleration is the rate of change in velocity • Acceleration refers to the change in velocity over a period of time Think about it… if velocity is the change in displacement over a period of time, what do you think the formula for acceleration is?

  5. Acceleration • Q: What is the symbol for acceleration? • A: a • Q: What is the formula for acceleration? • A: • Q: What are the units of measurement for acceleration? • A: m/s2 

  6. Acceleration and Newton • Sir Isaac Newton (1643-1727) came up with several key formulas that help us understand the world around us. His second law applies to what we’re learning now: • In simple terms, this formula tells us that FORCE IS ACCELERATION… so acceleration is just a push or pull on an object that causes it to change the velocity it’s moving at Force = a push or a pull

  7. Reminder First, establish which direction is positive and which direction is negative: West East Left -------------------------- Right South---------------------------- North Down Up

  8. Acceleration = Force • Acceleration = force (a push or a pull)… so to figure out if the acceleration is + or – just think of what direction you would have to push someone to change their velocity

  9. Pushing Demonstrations! • Stand up and push your chairs in. Make sure the aisles are clear • Grab a partner. Look them in the eye and say, “I trust you.” • Listen to Ms. T for directions

  10. Example A Velocity Direction Δv = vf - vi Acceleration + 2 m/s to + 6 m/s • --------------------------------------------------------------- vivf + + 6 – 2 = + 4 m/s +

  11. Example B Velocity Direction Δv = vf - vi Acceleration + 8 m/s to + 1.5 m/s • ------------------------------------------------------------- vivf + + 1.5 – 8 = - 6.5 m/s -

  12. Example C Velocity Direction Δv = vf - vi Acceleration - 7 m/s to -3 m/s ------------------------------------------------------------- vf vi _ _ -7 – (-3) = - 4 m/s _

  13. Example D Velocity Direction Δv = vf - vi Acceleration 0 m/s to -9 m/s ------------------------------------------------------------- vf vi _ _ 0 – (-9) = +9 m/s +

  14. Acceleration Word Problems • A skater goes from a standstill to a speed of 6.7 m/s in 12 seconds.  What is the acceleration of the skater? a = vf – vi tf – ti a = 6.7 12 12 a = 6.7 – 0 12 - 0 a = 0.6 m/s2

  15. Acceleration Word Problems • During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25s.  What is the sprinter’s average acceleration during this period? a = vf – vi tf – ti a = 2.5 1.25 a = 7.5 – 5 1.25 - 0 a = 2m/s2

  16. Acceleration Word Problems • You are hiking down a mountain at -3.5 m/s when you start getting chased by zombies. You speed up to -9.7 m/s really quickly (like, in 5 seconds). What is your acceleration? a = vf – vi tf – ti a = -6.2 5 a = -9.7 – (- 3.5) 5 - 0 a = -1.24 m/s2

  17. Acceleration Word Problems A baby sitter pushing a stroller starts from rest and accelerates at a rate of  0.457m/s2.  What is the velocity of the stroller after it has traveled for 36 seconds? Δv = a x Δt Δv = 0.457 x 36 Δv = 16.452 m/s vf = Δv + vi vf = 16.452 + 0 vf = 16.452 m/s

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