Acceleration 1D motion with Constant Acceleration Free Fall Lecture 04 (Chap. 2, Sec. 6-10 )

1. General Physics (PHYS101) Acceleration 1D motion with Constant Acceleration Free Fall Lecture 04 (Chap. 2, Sec. 6-10 ) Sections 30 and 33 are canceled and became section 27

2. Lightning Review Last lecture: • Displacement - change of position • Average velocity - displacement over time interval • Instantaneous velocity - the same but for very small time interval

3. Average Acceleration • Average acceleration is the rate of change of the velocity SI unit: m/s2 • Changing velocity (non-uniform) means an acceleration is present • Average acceleration is a vector quantity (i.e described by both magnitude and direction)

4. Instantaneous Acceleration • Instantaneous acceleration is the limiting case of the average acceleration as the time interval goes to zero.

5. Graphical Interpretation of Acceleration • Average acceleration is the slope of the line connecting the initial and final velocities on the velocity-time graph • Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph for the given value of time

6. 1D motion: uniform velocity • Uniform velocity (shown by red arrows maintaining the same size) • Acceleration equals zero

7. 1D motion: constant (positive) acceleration • Velocity and acceleration are in the same direction • Acceleration is uniform (blue arrows maintain the same length) • Velocity is increasing in time (red arrows are getting longer)

8. 1D motion: constant (negative) acceleration • Velocity and acceleration are in opposite directions • Acceleration is uniform (blue arrows maintain the same length) • Velocity is decreasing (red arrows are getting longer)

9. 1D motion: constant acceleration Our job:to find the equation for the position and velocity of the object to make predictions!

10. v x x0 t t 1D motion with constant acceleration • Recall that • We know that v0 • We find • Since

11. 1D motion with constant acceleration

12. acceleration is constant velocity as a function of time velocity as a function of displacement displacement as a function of velocity and time Displacement as a function of velocity average velocity displacement as a function of time Summary of kinematic equations: 1D motion

13. Free fall - 1D motion with constant acceleration

14. 0 y x 0 2 1 3 1 2 3 y Free fall - 1D motion with constant acceleration • All objects moving under the influence of only gravity are said to be in free fall • All objects falling near the earth’s surface fall with a constant acceleration • This acceleration is called gravitations acceleration, indicated by g and always points perpendicular to the earth’s surface

15. acceleration displacement vs velocity and time displacement vs time displacement vs velocity velocity vs time velocity vs displacement average velocity Free fall - 1D motion with constant acceleration

16. y Case 1:zero initial velocity

17. Case 1 y y Case 2:NONzero initial velocity Case 2

18. Case 3: object thrown upward

19. Case 4: object thrown upward

20. Free fall • Mass does not matter, if the air resistance is neglected

21. Positive acceleration

22. Negative acceleration

23. 1D motion with constant acceleration • Example 1: A car is traveling with a constant speed v0. At some time, the driver puts on the brakes, which slows the car down at a rate of a. • Find: • how much farther does the car travel for time tf, before it stops completely. • low long does it travel if the stopping distance is xf. Given: v0=v0 a=-a x0=0 t0=0 v=0 Find: 1) xf=?, knowing tf. 2) tf=?, knowing xf.