Constant, average and Instantaneous Velocity

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Presentation transcript:

Constant, average and Instantaneous Velocity Position-Time and Velocity-Time Graphs

Motion Uniform motion Non-uniform motion Velocity (rate of change of position) remain constant Non-uniform motion Velocity is changing (in magnitude, direction or both

Average Velocity When calculating average velocity only the final and initial velocity are considered. One is not sure what has occurred in between these data points

Constant Velocity When calculating the constant velocity of an object all changes during the time interval are considered. The data points are organized into a table and a position-time graph is plotted

Average Velocity vrs. Constant Velocity Open text to page 49 and compare figure 2.13 and 2.14 Pre-lab – page 50 (to do on Thursday) Web site exercise – PT graphs

Position-Time Graphs Position on y axis Time on x axis Slope = velocity (steeper the line, higher the velocity Change of direction (moving towards zero) Velocity = zero (horizontal line)

Instantaneous Velocity The velocity at a specific point in time. It is the slope of a tangent to the curve of a PT graph Model problem (page 55) Do questions 4 and 5 page 57 Do questions 1-3, 5 and 6 page 60

Acceleration A vector quantity that describes the rate of change in velocity The quotient of change in velocity and the time interval over which the change takes place a = Δv/t v – velocity (m/s) t – time (s) a – acceleration (m/s/s or m/s2)

Example: Truck v = 20 m/s [E] a= 1.5 m/s2 [E] Start finish V= 20 m/s [E] 21.5 m/s [E] 23 m/s [E] T= 0s 1s 2s

An object can accelerate without either speeding up or slowing down… The direction of the acceleration vector is the direction of the change in velocity and not the direction of the velocity itself See figures on page 62 Increase velocity (pos. acceleration) Decrease velocity (neg. acceleration) An object can accelerate without either speeding up or slowing down…

If the magnitude of the velocity does not change but the direction does, the object is accelerating

Uniform vrs. Non-Uniform Acceleration Velocity v=Δd/t slope on a PT graph with curving graph use a tangent to find instantaneous velocity can be constant or non-uniform Acceleration a = Δv/t slope on a VT graph with curving graph use a tangent to find instantaneous velocity can be constant or non-uniform

Notice that we use the terms constant, average and instantaneous acceleration Check out fig. 2.22 on page 64