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

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1Motion along a straight line:Position, Displacement and Velocity

Lecture 03General Physics (PHYS101)www.cmt.ua.ac.be/golib/PHYS10121D motionThe 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/PHYS1013Coordinate SystemsCoordinate systems are used to describe the position of an object in spaceCoordinate system (frame) consists of:0x12345(cm)instructions on how to label a point relative to the origin and the axesa fixed reference point called the originspecific axes with scales and labels4PositionThe position (x) of an object describes its location relative to some origin or other reference point (frame of reference)0x1Frame AThe position of the red ball differs in these two coordinate systems 0x2Frame B5PositionExample:The position of the ball is x=+2 cmThe position of the ball is x=-2 cmNote: (a) the + indicates the direction to the right of the origin;(b) the - indicates the direction to the left of the origin0x (cm)123-1-2-30x (cm)123-1-2-36

DisplacementDisplacement 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 1D7

Displacement

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0x (cm)1234-1-2-3-4Displacement0x (cm)1234-1-2-3-40x (cm)1234-1-2-3-4

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

displacementdistance10

Distance or Displacement? 1011Position vs time graphsPosition vs time graph is not necessary a straight line, even through the motion is one dimensional.

50x (m)607080904030201001250x (m)60708090403020100Average velocityIt takes time for an object to undergo a displacementThe 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/s13

Average velocityExample: Suppose that in both cases truck covers the distance in 10 sec.

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Velocity vs SpeedAverage speed = total distance / total time. SI unit m/s.50x (m)60708090403020100Speed 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 m15Graphical Interpretation of Average VelocityVelocity can be determined from a position vs time graphAverage velocity equals the slope of the line joining the initial and final positions.

16Instantaneous velocity

x=400 kmt=4 hv=x/t =100 km/h

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

18Graphical Interpretation of Instantaneous VelocityInstantaneous 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

19Average vs Instantaneous velocity

Can these velo-cities be equal?20Uniform Velocity Uniform velocity is constant velocityThe instantaneous velocities are always the sameAll the instantaneous velocities will also equal the average velocitypositiontimevelocitytime21Velocity vs time graph The area under a velocity vs time graph gives the displacement for a given interval of timevelocitytime22

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.S1S22223

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 timeInstantaneous velocity - velocity at a given timeUniform velocity - instantaneous velocity is the same as the average velocity and the speed represents their magnitude.24Average vs. instantaneous velocity