# Motion in One Dimension Average Versus Instantaneous.

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Motion in One Dimension Average Versus Instantaneous

Position-Time Graph  Where is the animal at time t = 0?  What time corresponds to a position of zero?

Slope of a Position-Time Graph  What is the slope of a position-time graph?  Is this graph constant velocity or not?  What would the velocity-time graph look like for the graph on the last slide?

Distance Versus Displacement  Which one is a vector quantity?  What is the displacement?  What is the distance traveled?

Average Velocity  Average Speed is total distance divided by total time or the average slope of the line or curve  Instantaneous Speed

Graphing Position-time graph—slope is the speed Velocity-time graph—slope is the acceleration

Slopes  Velocity  Acceleration

Problem  A car is located at 30 m at point A, 50 m at point B, 40 m at point C, 0 m at point D, -40 m at point E and –50 m at point F. Equal time intervals separate each point. Sketch the position versus time graph. Find the displacement, average velocity and average speed of the car between A and F.

Problem 2  A particle moves along the x-axis. Its position varies with time according to the expression x = -4t + 2t 2 where x is in meters and t is in seconds. A)Determine the displacement of the particle in the time intervals t = 0 to t = 1 sec and t = 1 sec to t = 3 sec. B) Calculate the average velocity during these two time intervals. C) Find the instantaneous velocity at time t = 2.5 sec.

Problem 3  The position of an object is given by the equation x(t) = 2 + 4t – t 2, where position is measured in meters and time in seconds. What is the particle’s average acceleration from t = 0 to t = 2?

Homework  Chapter 2  Questions 1,5,7  Problems 2,5,7,11,16,19

Unique Situation Equations  All of these equations assume constant acceleration:

Derive These

Derive Some More

Gravity  Acceleration is a constant, g.  All these equations apply.

Homework  Problems 23, 29, 32, 35, 38, 39, 41, 44, 47, 55, 57, 62

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