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? 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. 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 + + - - + - - + - or + 0 0 - or + 0 0 Motion Analyze the Following Graph Velocity vs. Time Graph For cases with constant acceleration 𝑣𝑎𝑣𝑔 = 𝑣𝑖 −𝑣𝑓 2 & 𝑣𝑎𝑣𝑔 = ∆𝑥 ∆𝑡 Set these two equations equal to one another and solve for Δx. Displacement with Constant Acceleration 1 ∆𝑥 = 𝑣𝑖 − 𝑣𝑓 ∆𝑡 2 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 = 𝑣𝑓 −𝑣𝑖 ∆𝑡 Solve for 𝑣𝑓 in terms of a. Velocity with Constant Acceleration 𝑣𝑓 = 𝑣𝑖 + 𝑎∆𝑡 One more… We know: 1 ∆𝑥 = 𝑣𝑖 + 𝑣𝑓 ∆𝑡 2 & 𝑣𝑓 = 𝑣𝑖 + 𝑎∆𝑡 Solve for a new Δx. Displacement with Constant Acceleration 1 ∆𝑥 = 𝑣𝑖 ∆𝑡 + 𝑎 ∆𝑡 2 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 1 ∆𝑥 = 𝑣𝑖 − 𝑣𝑓 2 𝑣𝑓 = 𝑣𝑖 + 𝑎∆𝑡 1 ∆𝑥 = 𝑣𝑖 ∆𝑡 + 𝑎 ∆𝑡 2 vf2 = vi2 + 2aΔx 2