1. Acceleration in 1-D

2. What causes acceleration?
What is acceleration? Change in velocity This includes a change in magnitude or direction What causes acceleration? A Force

3. where aav = average acceleration Δv = change in velocity Δt = time
→ →
aav = Δv Δt →
where aav = average acceleration
Δv = change in velocity
Δt = time

4. → → 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.

5. Equations
For any accelerated motion, we use the constant acceleration equations

6. Kinetic Equations:
→ → →
v2 = v1 + a Δt
→ → →
2. Δd = (v2 – v1) Δt 2

7. Kinetic Equations:
→ → → 3. Δd = v a Δt2 → → → 4. Δd = v2 – 0.5 a Δt2 → → → → 5. v22 = v a Δd

8. 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?

9. Acceleration in 2-D 𝑎 = 𝑣 2 − 𝑣 1 ∆𝑡
𝑎 = 𝑣 2 − 𝑣 1 ∆𝑡
Since these are vectors, we must use vector subtraction
𝑣 𝐴𝐵 =− 𝑣 𝐵𝐴
𝑎 = 𝑣 2 +(− 𝑣 1 ) ∆𝑡
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

10. 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?

11. 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 32o N]. What is Arnav’s acceleration?