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# 1.3 velocity

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IB physics - velocity

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### 1.3 velocity

1. 1. LECTURE 3 Velocity IB Physics Power Points Topic 2 Kinematics www.pedagogics.ca
2. 2. Velocity vs. Speed Velocity is a vector quantity and is defined as the change in an object’s position per unit of time. Velocity and speed are not the same thing and quite often have different values. Speed is a scalar quantity and is defined as the distance travelled by an object per unit of time. s v = t   displacement velocity = time distance speed = time s v = t  
3. 3. Starbucks final position Initial position 3 km [South] House 2 km [North] Velocity Remember Victor, he walked 5 km North to his friends house in 2 hours and then 2 km South to Starbucks in 1 hour. What was Victor’s average velocity and speed? Speed s 7 km v = 2.3 km/hr t 3 hr     s 3 km [N] v = 1 km/hr [N] t 3 hr    
4. 4. -3 -2 -1 0 1 2 3 0 1 2 3 4 time (hrs) Position[N]km Velocity from Position-Time Graphs Start Friend’s house Starbucks Velocity can be determined from the slope of a line drawn on a position time graph. For Victor’s walk: A line can be drawn between Victor’s start and finish points The slope value is the average velocity 3 km [N] Slope = 1 km/hr [N] 3 hr rise run  
5. 5. An example: The average velocity for the entire trip shown in this position-time graph is ZERO! Why? /m [N] s /s t TIP: Don’t confuse average velocity with a mean value calculation  we are not adding up a number of velocity measurements and dividing by the number.
6. 6. 0 100 200 300 400 500 600 0 5 10 15 t /s s/m[downwards] Straight lines on a position-time graph indicate uniform motion (CONSTANT VELOCITY). A change in slope or a curved line indicate that velocity is changing. Any object that undergoes a velocity change is experiencing an ACCELERATION. This position-time graph shows the velocity increase of a falling ball. In this case, the increase in velocity implies an acceleration.
7. 7. 0 100 200 300 400 500 600 0 5 10 15 t /s s/m[downwards] One way to determine the velocity from this graph is to calculate the slope of tangent lines. The slope of a tangent indicates the INSTANTANEOUS velocity at that instant in time. Velocity at t = 2 s Velocity at t = 8 s
8. 8. The slope of a tangent can be difficult to determine accurately. Fortunately there is an easier way. For objects that are accelerating uniformly, the instantaneous velocity at the middle of a time interval is the same as the average velocity for the time interval. On a graph this looks like this
9. 9. The average velocity of the time interval t = 2  6 s can be determined by the slope of the red line. t = 4 s t = 2 s t = 6 s vavg 2-6 s= vinst 4 s 4 seconds is halfway through the time interval of 2  6 s. The instantaneous velocity at t = 4 s is the same as the average velocity for the interval. SLOPES ARE PARALLEL vavg 3-5 s= vinst 4 s
10. 10. Velocity-Time Graphs A velocity-time graph shows how the velocity of an object changes with time. v t s t This position-time graph shows an object moving away from a reference point at a constant velocity. How do we know? This velocity-time graph corresponds to the same object. Note constant velocity (how is this indicated?)
11. 11. Velocity-Time Graphs What would the corresponding velocity-time graph be for a ball being tossed in the air? t S [up] t v [up]
12. 12. Velocity-Time Graphs A car at rest (0 ms-1) increases its velocity by 1 ms-1 each second. What would the velocity-time graph look like? V t What would the slope of this graph tell us? t v rise v slope run t     The slope would give us the rate of change of the velocity (units would be ms-1/s i.e. meters per second per second or ms-2). The rate that velocity changes with time is called ACCELERATION.
13. 13. Velocity-Time Graphs 0 5 10 15 20 25 30 0 5 10 15 20 25 time /s position/m[North] Practice: Calculate the velocity of this object in each distinct section of the following position-time graph. -1 1 2 ms [N]v  -1 2 0 msv   -1 3 2.5 ms [S]v -1 4 0 msv   -1 5 4.4 ms [N]v
14. 14. Velocity-Time Graphs Practice: Sketch the corresponding velocity time graph. -3 -2 -1 0 1 2 3 4 5 0 5 10 15 20 25