1Dkinematics

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Chapter 2

Motion Along a Straight Line

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Displacement vs distance

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Question

TRUE or FALSE:

The displacement of an object for a round trip between two locations is always greater than zero.

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Question

TRUE or FALSE:

The displacement of an object during any time interval is always greater than or equal to the distance it travels during the same time interval

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Example. The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D.

• Use the diagram to determine the resulting displacement and the distance traveled by the skier during these three minutes.

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• Now for a final example. A football coach paces back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D.

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Question

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Velocity and Speed

Speed – “how fast the object is moving” velocity – “the rate at which the body changes position”

http://www.physicsclassroom.com/Class/1DKin/U1L1d.html

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Average Velocity, Average Speed

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Example

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Question

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Archimedes ran 100m for 12s towards the positive x-direction. He backtracked 50m walking for 30s. What is his average speed? What is his average velocity?

Example

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Average and Instantaneous speed

Average speed – just distance over time (average of all inst. speeds)

Instantaneous speed – speed at a particular instant of time

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Average and Instantaneous speed

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Question

An object moves along the x-axis as shown in the figure. At which point is the magnitude of its velocity minimum?

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Question

Scooby doo cannot understand the difference between average and instantaneous velocity. Help Scooby by explaining to him like you would a 2nd year high school student and give an example of each.

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Acceleration

The rate of change in velocity

Could be:

1. change in the magnitude 2. change in direction

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Acceleration

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Average and instantaneous acceleration – using v-t graph

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Average and instantaneous acceleration – using v-t graph

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Comparing accelerations

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Comparing accelerations – using ticker tapes

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Comparing accelerations – using x-t graphs

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Comparing accelerations – using v-t graphs

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Graphical analysis of a particle’s motion

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Question

Can an object have zero velocity and still be accelerating?

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Motion with constant acceleration

Average velocity

0

2avev v

v

0

avex x

vt

True only for motions with constant acceleration

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Motion with constant acceleration

20 0

12

x x v t a t

0v v a t

2 20 2v v a x

Kinematic equations

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Example

Toto, a famous drag racer, revved up his car and traveled along a straight horizontal road accelerating from rest at 2 m/s towards the East. What is Toto’s velocity after 5 s? What is his displacement from his initial position x=0m after 5 s?

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Question

TRUE or FALSE

The kinematic equations are ALWAYS valid.

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Free-falling bodies

Presence of gravitational force due to Earth causes the ball to accelerate.

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Free-falling bodies

Acceleration due to gravity NEAR the Earth’s surface

29 81 ms

g .

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Free-falling bodies

Negative sign of the gravitational acceleration indicates “downward” direction.

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Free-falling bodies

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Kinematic Equations for free-falling objects

20 0

12

x x v t a t

0v v a t

2 20 2v v a x

Free-fallIn general

20 0

12

y y v t g t

0v v g t

2 20 2v v g y

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Kinematic Equations for free-falling objects

20 0

12

y y v t g t

0v v g t

2 20 2v v g y

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Question

True or false:Two identical objects will fall with the

same acceleration.

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Question

What if these two identical objects were joined together, what happens to their acceleration? Will it double? Will be halved? Will remain the same?

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Question

If you drop an object in the absence of air resistance, it accelerates downward at 9.8m/s2. If instead you throw it downward, its downward acceleration after release is

a) Less than 9.8m/s2

b) 9.8m/s2

c) more than 9.8m/s2

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Example

Zoe, the red, falls over a 20.0-m ravine. What is the vertical component of his velocity right before he hits the ground?

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Question

An object falling near the surface of the earth has a constant acceleration of 9.8m/s2. What does this mean? Help Coyote puzzle this over before Roadrunner surprises him and Coyote falls off the cliff.

1Dkinematics

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