2.2 Acceleration Physics A

Objectives I can describe motion in terms of changing velocity. I can compare graphical representations of accelerated and non-accelerated motions. I can apply kinematic equations to calculate distance, time or velocity under conditions of constant acceleration.

What are the units on acceleration?

Tip: Watch for implied data in the problems. Practice Problem 1 With an average acceleration of -1.2 m/s2, how long will it take a cyclist to bring a bicycle with an initial speed of 6.5 m/s to a complete stop? Tip: Watch for implied data in the problems.

At the bottom of page 50 1, 2, and 3 Conceptual Challenge At the bottom of page 50 1, 2, and 3

Identify which values represent: speeding up, slowing down, constant velocity, speeding up from rest, or remaining at rest. Table 3 Velocity and Acceleration vi a Motion + - - or +

Analyze the Following Graph

Velocity vs. Time Graph

For cases with constant acceleration 𝑣 𝑎𝑣𝑔 = 𝑣 𝑖 − 𝑣 𝑓 2 & 𝑣 𝑎𝑣𝑔 = ∆𝑥 ∆𝑡 Set these two equations equal to one another and solve for Δx.

Displacement with Constant Acceleration ∆𝑥= 1 2 𝑣 𝑖 − 𝑣 𝑓 ∆𝑡

Practice C 1. A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance the car travels during this time.

More useful equations: We know: 𝑎= ∆𝑣 ∆𝑡 = 𝑣 𝑓 − 𝑣 𝑖 ∆𝑡 Solve for 𝑣 𝑓 in terms of a.

Velocity with Constant Acceleration 𝑣 𝑓 = 𝑣 𝑖 +𝑎∆𝑡

One more… We know: ∆𝑥= 1 2 𝑣 𝑖 + 𝑣 𝑓 ∆𝑡 & 𝑣 𝑓 = 𝑣 𝑖 +𝑎∆𝑡 Solve for a new Δx.

Displacement with Constant Acceleration ∆𝑥= 𝑣 𝑖 ∆𝑡+ 1 2 𝑎 ∆𝑡 2

Practice D Do problems 1-4

Final Velocity after any Displacement vf2 = vi2 + 2aΔx

Practice E Problems 2 & 4

Equations for Constantly Accelerating 1-D Motion ∆𝑥= 1 2 𝑣 𝑖 − 𝑣 𝑓 𝑣 𝑓 = 𝑣 𝑖 +𝑎∆𝑡 ∆𝑥= 𝑣 𝑖 ∆𝑡+ 1 2 𝑎 ∆𝑡 2 vf2 = vi2 + 2aΔx