Motion along a straight line: Position , Displacement and Velocity Lecture 03

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

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

3. 2 4 5 1 3 Coordinate Systems • Coordinate systems are used to describe the position of an object in space • Coordinate system (frame) consists of: • a fixed reference point called the origin • specificaxes with scales and labels • instructions on how to label a point relative to the origin and the axes 0 x (cm)

4. Frame B Frame A x2 0 x1 0 Position • The position (x) of an object describes its location relative to some origin or other reference point (frame of reference) • The position of the red ball differs in these two coordinate systems

5. x(cm) x(cm) -3 -2 -1 0 2 1 3 -3 -2 -1 0 2 1 3 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

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

7. Displacement

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

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

10. Distance or Displacement? 10

11. Position vs time graphs x (m) 0 10 20 30 40 50 60 70 80 90 • Position vs time graph is not necessary a straight line, even through the motion is one dimensional.

12. SI unit: m/s • The direction ofwill be the same as the direction of the displacement( is always positive). x (m) 0 10 20 30 40 50 60 70 80 90 Average velocity • It takes time for an object to undergo a displacement • The average velocity is the rate at which the displacement occurs

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

14. x (m) 0 10 20 30 40 50 60 70 80 90 Velocity vs Speed s=160 m • Average speed = total distance / total time. SI unit m/s. • Speed is a scalar quantity (no information about sign/direction of motion is needed) • In some cases speed is the magnitude of the velocity.

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

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

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

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

22. S1 S2 Velocity vs time graph 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.? 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. 22

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. Average vs. instantaneous velocity