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