1 Velocity and Acceleration

2 1. Frame of Reference

3 Frame of Reference – how you determine the position. We normally use N-S-E-W. Our Reference:  Positive, (+) Moving RIGHT  or Moving UP   Negative, (-) Moving LEFT  or Moving DOWN   If you are not sure of the direction, use Positive(+)  Choose your starting position as Zero (0), unless the problem tells you otherwise!

4 Scalar Quantity -  Magnitude - “How much”  Direction does not matter  Mass, temperature, and time are scalar quantities

5 Vector Quantity –  Magnitude AND Direction  How much and which way  Velocity, force and displacement are vector quantities.  Use “vector diagrams” to represent these quantities.

6  The arrow shows the direction  Length of arrow is proportional to the magnitude.  High velocity to the right  Low velocity to the left Position – your location using the frame of reference. Ships use longitude and latitude.  Symbol is d for horizontal motion. (your book uses x)  Vector quantity – magnitude and direction.  I am located 5 km south of home.

7 Displacement – change in position  “How far out of place an object is”  Symbol is  d (x-horizontal, y-vertical)   “delta” is “change in”  d = d f - d i  Vector Quantity: Magnitude and Direction  Units include m (meter), km, cm, mm  You travel 10 km East  Displacement = zero (0) when you return to the original position. You are not “out of place”

8  You travel 10 km East, stop and then turn around and travel 10 km West. Displacement,  d = 0 10 km East 10 km West Displacement =  d = 0  You travel 10 km East, stop and then turn around and travel 15 km West. 10 km East 15 km West Displacement =  d = -5km

9 Distance  How far you traveled  Scalar quantity  Magnitude only  I drove 20 km today.  10 km East 10 km West Distance Traveled = 20 km  10 km East 15 km West Distance Traveled = 25 km

10 Time  Clock reading  Scalar Quantity  Symbol is t  Units include seconds, minutes, hours, days Time Interval  Elapsed time, change in time  Symbol  t  Scalar Quantity   t = t f – t i (final time – initial time)  Units include seconds, minutes, hours, days

11 2. Velocity Motion – Change in position Average Velocity  Rate of change in position  =  

12  Vector Quantity – Magnitude and Direction We will use positive (+) and negative (-) to show direction  +  right or up  -  left or down  + moving towards you (you are the reference)  - moving away from you  Average velocity does not indicate what happens during the time interval. You could have stopped, sped up, or even slowed down.

13 Instantaneous velocity – the velocity at any given instant in time. Constant velocity - all the instantaneous velocities are equal. “Cruise Control” Only true judgment of velocity is a reference point that is not moving.

14 Overall Velocity  Moving Sidewalk +3m/s You walk on it +1 m/s Overall velocity +4m/s  Moving sidewalk +3m/s You walk backwards -1m/s Overall velocity +2m/s Speed – scalar quantity, distance traveled over a period of time. No indication of direction!

15 3. Acceleration Average Acceleration  Rate of change in velocity  Toughest time to walk on the bus? When it is speeding up or slowing down!

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17 AAverage acceleration =  v f = final velocity v i = initial velocity UUnits : NNOT!!

18  Vector Quantity – magnitude and direction  If you are moving right or up  and Speeding Up : +a (positive acceleration) Slowing Down : -a (negative acceleration) This is normal conditions!  If you are moving left or down  and Speeding Up : -a (negative acceleration) Slowing Down : +a (positive acceleration)  If you do not know direction left or right use Speeding Up : +a Slowing Down : -a

19 Just remember :  The direction of the acceleration vector depends on : Whether the object is speeding up or slowing down. Whether the object is moving in the positive (+) or negative (-) direction.  Rule of Thumb – If an object is slowing down, then its acceleration is in the opposite direction of its motion.

20  If you are moving from rest v i = 0 (zero)  If you are coming to a stop v f = 0 (zero)  If you are moving at constant velocity = 0 (cruise control)  If you are not moving : v = 0 Acceleration is not discussed! (aka a  0)