1. 1 Motion along a straight line: Position, Displacement and Velocity Lecture 03 General Physics (PHYS101) www.cmt.ua.ac.be/golib/PHYS101

2. 2 1D motion 1.The motion is along a straight line only. 2.Forces will not be considered. 3.Objects are considered as particles (a point-like objects) www.cmt.ua.ac.be/golib/PHYS101

3. 3 Coordinate Systems Coordinate systems are used to describe the position of an object in space Coordinate system (frame) consists of: 0 x 1 2 3 45 (cm) instructions on how to label a point relative to the origin and the axes a fixed reference point called the origin specific axes with scales and labels

4. 4 Position The position (x) of an object describes its location relative to some origin or other reference point (frame of reference) 0 x1x1 Frame A The position of the red ball differs in these two coordinate systems 0 x2x2 Frame B

5. 5 Position Example: The position of the ball is x=+2 cm The position of the ball is x=-2 cm Note: (a) the “+” indicates the direction to the right of the origin; (b) the “-” indicates the direction to the left of the origin 0 x (cm) 1 2 3 -2-3 0 x (cm) 1 2 3 -2-3

6. 6 Displacement Displacement is a vector quantity and needs a directional information Displacement is the measure of change in position. + or - is generally sufficient to indicate direction in 1D

7. 7 Displacement

8. 8 0 x (cm) 1 234 -2-3-4 Displacement 0 x (cm) 1 234 -2-3-40 x (cm) 1 234 -2-3-4 Distance:

9. 9 Distance or Displacement? Distance may be, but is not necessarily, the magnitude of the displacement. Distance - scalar quantity. Displacement - vector quantity. displacementdistance

10. 10 Distance or Displacement? 10

11. 11 Position vs time graphs Position vs time graph is not necessary a straight line, even through the motion is one dimensional. 50 x (m) 60 708090 403020100

12. 12 50 x (m) 60 708090 403020100 Average velocity It takes time for an object to undergo a displacement The average velocity is the rate at which the displacement occurs The direction of will be the same as the direction of the displacement ( is always positive). SI unit: m/s

13. 13 Average velocity Example: Suppose that in both cases truck covers the distance in 10 sec.

14. 14 Velocity vs Speed Average speed = total distance / total time. SI unit m/s. 50 x (m) 60 708090 403020100 Speed is a scalar quantity (no information about sign/direction of motion is needed) In some cases speed is the magnitude of the velocity. s=160 m

15. 15 Graphical Interpretation of Average Velocity Velocity can be determined from a position vs time graph Average velocity equals the slope of the line joining the initial and final positions.

16. 16 Instantaneous velocity ∆x=400 km ∆t=4 h v=∆x/∆t =100 km/h

17. 17 Instantaneous Velocity Instantaneous velocity is defined as the limit of the average velocity as the time interval becomes infinitesimally short, or as the time interval approaches zero The instantaneous velocity indicates what is happening at every point of time

18. 18 Graphical Interpretation of Instantaneous Velocity Instantaneous velocity is the slope of the tangent line to the position vs time curve at the time of interest Instantaneous speed is the magnitude of the instantaneous velocity

19. 19 Average vs Instantaneous velocity Can these velo- cities be equal?

20. 20 Uniform Velocity Uniform velocity is constant velocity The instantaneous velocities are always the same All the instantaneous velocities will also equal the average velocity position time velocity time

21. 21 Velocity vs time graph The area under a velocity vs time graph gives the displacement for a given interval of time velocity time

22. 22 Example: Speedometer readings are obtained and graphed as a comes to a stop sign along a straight-line path. How far does the car move between t=0 and t=16 sec.? Velocity vs time graph Solution: Since there is not a reversal of direction, the area between the curve and the time axis will give the distance traveled. Thus, the car travelled 160 m distance. S1S1 S2S2 22

23. 23 Summary: Motion in 1D Displacement - change of position in time Displacement is not necessary the distance! Velocity is not necessary the speed! Average velocity - rate of change of position in time Instantaneous velocity - velocity at a given time Uniform velocity - instantaneous velocity is the same as the average velocity and the speed represents their magnitude.

24. 24 Average vs. instantaneous velocity