What is a Vector A vector is a

Direction • In one dimensional space, we may use a sign to denote the

Distance vs. Displacement does not depend on the path taken, only the initial and

Distance vs. Displacement • Distance is the total length of the path taken •

Distance vs. Displacement If a student drives 4 miles from home to school, and,

Distance vs. Displacement What was his displacement? What was the total distance traveled? meters

Velocity - Example Your third period classroom is 150 m away from your second

Acceleration Even if an object is traveling at a constant speed, if the direction

Acceleration vs. Deceleration • Deceleration – speed is decreasing • Deceleration occurs when the

Acceleration vs. Deceleration Example: A falling apple experiences a negative acceleration because it is

Free-Fall Symmetry • Free-fall problems exhibit a natural symmetry

Free-Fall Symmetry How long does it take for the object to return to its

Graphical Analysis – Instantaneous Velocity

Graphical Analysis – Constant Acceleration

Graphical Analysis Recall that the product of two values can be visualized as the

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What is a Vector? • A vector is a mathematical object which describes magnitude and direction • We frequently use vectors when solving problems in Physics Example: • Change in position (displacement) • Velocity

Notation

Direction • In one dimensional space, we may use a sign to denote the vector’s direction • For this sign to have any meaning, we must define the positive and negative directions N • For Example Up Down W E S

Displacement

Displacement meters

Distance vs. Displacement does not depend on the path taken, only the initial and final positions All three paths have the same displacement

Distance vs. Displacement • Distance is the total length of the path taken • Distance does depend on the path • An odometer measures distance Which path has the shortest distance?

Distance vs. Displacement If a student drives 4 miles from home to school, and, at the end of the day, 4 miles from school back home. What was his displacement? What was the total distance traveled?

Distance vs. Displacement What was his displacement? What was the total distance traveled? meters

Velocity

Velocity vs. Speed

Velocity - Example

Velocity - Example Your third period classroom is 150 m away from your second period classroom. You have four minutes between classes. Assuming you walk in a direct path, at this same speed, will you make it to class on time?

Velocity - Example

Velocity - Example West 2 East 4 8 km

Acceleration

Acceleration Even if an object is traveling at a constant speed, if the direction of the motion changes, the object is accelerating.

Acceleration vs. Deceleration • Deceleration – speed is decreasing • Deceleration occurs when the acceleration opposes the motion • Deceleration is not the same as negative acceleration

Acceleration vs. Deceleration Example: A falling apple experiences a negative acceleration because it is falling downward. Up However, the apple is not decelerating. Down

Acceleration – Example

Constant Acceleration

Constant Acceleration - Example