Motion in One Dimension Average Versus Instantaneous.
Transcript of Motion in One Dimension Average Versus Instantaneous.
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
txv /
t 0v x tlim /
v dx dt /
Graphing
•Position-time graph—slope is the speed
•Velocity-time graph—slope is the acceleration
Slopes
Velocity Acceleration
v dx dt /
a dv dt /
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 + 2t2 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 – t2, 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:
v v ato
v v a xo
2 2 2
x v t ato 1
22
Derive These
a dv dt /
dv adt
dv a dt
v at C
dv adtt
v a C
v C
v v ato
o
0
00 ( )
Derive Some More
dx vdt
dx vdt
dx v at dt
x v t at
o
o
( )
/1 2 2
Gravity
Acceleration is a constant, g. All these equations apply.
Homework
Problems 23, 29, 32, 35, 38, 39, 41, 44, 47, 55, 57, 62