Velocity and Acceleration

1. Velocity and Acceleration

2. Speed vs.Velocity • Speed (s) is the distance an object travels per unit of time (rate). • Velocity (v) describes the speed and direction of a moving object.

3. Velocity • Objects undergoing motion will either have a constant or changing velocity • constant velocity = not speeding up or slowing down. • changing velocity = speeding up or slowing down.

4. Distance (m) Time (s) Constant / Zero Velocity Zero Velocity Constant velocity

5. Distance (m) Time (s) Changing Velocity Slow Down Speed up

6. Velocity Time Displacement Average Velocity • When working with a constant velocity, we use the following equation. νavg =Δx / Δt Δ = change

7. Sample Problem What is the velocity of a runner that can travel 10 m in 5 seconds? νavg =Δx / Δt νavg= 10 m/5 s νavg = 2 m/s

8. Velocity Time Acceleration changes velocity • Acceleration (a): the rate of change of velocity. • Objects can accelerate in both the + and - direction.

9. 100 velocity 0 Time Accelerating Car Constant acceleration

10. 100 velocity 0 Time Car on cruise control Zero Acceleration

11. 100 velocity 0 Time Negative Accelerating Car - acceleration

12. Final Velocity Initial Velocity acceleration Acceleration (cont.) aavg = Δ ν /Δt = vf – vi Δt SI unit = m/s²

13. Sample Problem A car traveling at 7.0 m/s accelerates uniformly to a velocity of 12.0 m/s in 2.0 s. What is the acceleration of the car? 2.5 m/s² a = vf – vi Δt = (12.0 m/s – 7.0 m/s) = 2.0 s Vf= 12 m/s Vi= 7 m/s t = 2.0 s

14. Forward Motion Zero Motion Velocity (v) Time (Δt) Reverse Motion Changing Acceleration

15. 1-Dimentional Motion Equations Vavg =Δx/Δt Δx = ½ (vi +vf) Δt a = (vf- vi) / Δt Δx = viΔt + ½ aΔt² vf² = vi² + 2aΔx