chapter 2 kinematics in one dimension mechanics – forces & motion kinematics – describes...

Chapter 2Chapter 2Kinematics in One

DimensionMechanics – forces & motionKinematics – describes motionDynamics – causes of motion (forces)

2.1 – Displacement2.1 – Displacement

Displacement – straight-line distance b/w start & stop position.

0xxx f

2.2 – Speed and Velocity2.2 – Speed and Velocity

timeElapsed

ntDisplaceme velocityAverage

t

xv

Speed – scalar, Velocity - vector

t

xv

t

0lim

Instantaneous velocity … take calculus…

2.3 – Acceleration2.3 – Acceleration

timeElapsed

yin velocit Changeonaccelerati Average

Acceleration – a change in velocity; speeding up, slowing down or direction

change.

t

va

Positive acceleration

Negative acceleration (deceleration)

ASSIGN:

Ch. 2 #2-18 (evens)

Page 52

A little about kinematics graphs…

The independent variable is normally plotted on the x-axis and the dependent on the y-axis.

Time is always the independent variable since it does not depend on anything.

We can graph how distance traveled depends on time but not how time depends on distance traveled

Position vs. Time for NO Acceleration

Slope = velocity

Is this object accelerating?NO, constant slope on d vs. t graph

Positive and Negative Velocity

Position vs. Time for Acceleration

Velocity vs. Time

Slope = accelerationIs this object

accelerating?YES, constant slope on v vs. t graph

2.6 – Freely Falling Bodies2.6 – Freely Falling Bodies

Freefall – when the only force acting on an object is gravity (downward).

This picture does not represent freefall, why?

2.6 – Freely Falling Bodies2.6 – Freely Falling Bodies

Neglecting air

resistance, all objects fall at the same rate.

2.6 – Freely Falling Bodies2.6 – Freely Falling Bodies

An object in freefall on earth has an acceleration equal to 9.8 m/s2 (32 ft/s2)

g = -9.8 m/s2

the acceleration due to gravity

2.6 – Freely Falling Bodies2.6 – Freely Falling Bodies

g = -9.8 m/s2

Time [sec] Acceleration (t) [m/s2]

Velocity (t) [m/s]

Displacement (t)[m]

0

1

2

3

4

9.8

9.8

9.8

9.8

9.8

0

9.8

19.6

29.4

39.2

0

4.9

19.6

44.1

78.4

tvd

2.4 – Kinematics Equations2.4 – Kinematics Equations

atvv f 0

advv f 220

2 2

21

0 attvd

t

dv

2.5 – Using Kinematics 2.5 – Using Kinematics EquationsEquations

Time [sec] Acceleration (t) [m/s2]

Velocity (t) [m/s]

Displacement (t)[m]

0

1

2

3

4

9.8

9.8

9.8

9.8

9.8

0

9.8

19.6

29.4

39.2

0

4.9

19.6

44.1

78.42

21

0 attvd atvv f 0

Equations are meant to simplify problems, “don’t re-invent the wheel.”

2.5 – Using Kinematics 2.5 – Using Kinematics EquationsEquations

Make a drawing of the situationDecide which directions are

positive and negative.

Write down the given variables

In freefall, a = g = -9.8 m/s2

ASSIGN:

Ch. 2 #22-46 (every other even)

Page 53

Chapter 2 Review Questions

1. Explain the difference between velocity and acceleration.

2. Two objects are thrown vertically into the air, first one and then, a bit later, the other. Is it possible for both objects to reach the same maximum height at the same time?

3. An object is dropped from rest. How fast is the object going after (a) 1 sec, (b) 2 sec, (c) 3.2 sec?

4. How far has the object dropped after (a) 1 sec, (b) 2 sec, (c) 3.2 sec?

Chapter 2 Review Questions

5. A person claims a hang time of 2 seconds. How high would this person jump if they really had this hang time?

6. A ball is thrown straight up into the air.

(a) What is the acceleration of the ball during the entire time?(b) What is the velocity of the ball at the peak of its path?(c) If the ball was thrown up with an initial speed of 16.5 m/s, how long was the ball in the air?

(d) How high did the ball reach?