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## Acceleration in 1-D

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**What causes acceleration?**What is acceleration? Change in velocity This includes a change in magnitude or direction What causes acceleration? A Force**→ →**• aav = Δv Δt → where aav = average acceleration → Δv = change in velocity Δt = time**→ →**j = Δa Δt → where j = jerk (constant) → Δa = change in acceleration Note: jerk is not a desired type of motion, so usually it is not analyzed.**Equations**• For any accelerated motion, we use the constant acceleration equations**Kinetic Equations:**→ → → • v2 = v1 + a Δt → → → 2. Δd = (v2 – v1) Δt 2**Kinetic Equations:**→ → → 3. Δd = v1 + 0.5 a Δt2 → → → 4. Δd = v2 – 0.5 a Δt2 → → → → 5. v22 = v12 + 2 a Δd**Example #1:**An SUV that goes 60 m [fwd] as it stops. The magnitude of the stopping acceleration is 3.0 m/s2. • What is the initial velocity? • What is the stopping time?**Acceleration in 2-D**• Since these are vectors, we must use vector subtraction • In other words, when we add vectors we place them head to tail • In order to subtract vectors, we reverse the direction of the negative vector and then add the two vectors**Example #2: (2D-acceleration)**A car goes around a turn with a constant acceleration. The car was going 15m/s [N] as it entered the turn and came out at 15m/s [W]. If the turn lasted 10 seconds, what is the acceleration around the turn?**Example # 3**Arnav travels at 34.5 m/s [E 20o N]. Over a period of 5.00s, he changes his velocity to 34.5 [W 32oN]. What is Arnav’s acceleration?