Motion Part 1: Motion and Speed

Speed is the distance an object travels per unit of time. To calculate speed: Speed = Distance ÷ Time Distance is in meters (m) Time is in seconds (s) Speed is in meters per second (m/s)

A snail takes 5.0 s to crawl across the ruler. Example 1 A snail takes 5.0 s to crawl across the ruler. Speed = 2.0 m/s Speed = Distance ÷ Time Speed = 0.07 m ÷ 5.0 s

A car drives 250 m in one minute. Example 2 A car drives 250 m in one minute. Speed = 4.17 m/s Speed = Distance ÷ Time Speed = 250 m ÷ 60 s

Use the Formula Triangle! d To calculate speed: To calculate time: To calculate distance: s = d / t t = d / s d = s x t

Distance vs. Displacement Distance and displacement are different. Distance How far an object moves in total. Displacement The distance and direction an object moves from a starting position.

Distance vs. Displacement Jeffrey, my distance was 176 meters! But Billy, your displacement was 1 meter! BEGIN END

Distance vs. Displacement 90 ft. Distance = 90 ft. Displacement = 90 ft.

Distance vs. Displacement 90 ft. 90 ft. Distance = 180 ft. Displacement =127 ft.

Distance vs. Displacement 90 ft. 90 ft. 90 ft. Distance = 270 ft. Displacement = 90 ft.

Distance vs. Displacement 90 ft. 90 ft. 90 ft. 90 ft. Distance = 360 ft. Displacement = 0 ft.

Any Questions?

Motion Part 2: Distance-Time Graphs

Graphing Speed The motion of an object can be graphed. A distance-time graph shows the motion of a certain object in line graph form. Time is plotted on the horizontal (X) axis Distance is plotted on the vertical (Y) axis

The slope of a distance-time graph is the speed Distance-Time Graphs The slope of a distance-time graph is the speed Time (s) Distance (m) 1 2 4 3 6 8 5 7 9 12 10 16

Distance-Time Graphs S = D ÷ T S = D ÷ T S = D ÷ T = 0 ÷ 4 = 0 m/s = 8 ÷ 4 = 2 m/s S = D ÷ T = 8 ÷ 2 = 4 m/s

Distance-Time Graphs Constant speed No speed Constant speed (moving away) No speed (standing still) Constant speed (moving closer) (and faster!)

Interpreting a D-T Graph (1) Analysis: Time (s) Distance (m) The distance (m) stays the same as the time (s) increases Therefore, the object is at rest (not moving)

Interpreting a D-T Graph (2) Analysis: The object is moving away from the reference point The object is moving at a constant speed The object is moving quickly Time (s) Distance (m)

Interpreting a D-T Graph (3) Analysis: The object is moving towards the reference point The object is moving at a constant speed The object is moving slowly Time (s) Distance (m)

Interpreting a D-T Graph (4) Analysis: In Part A, the object is moving away at a constant speed In Part B, the object is at rest In Part C, it is moving towards at constant speed Time (s) Distance (m) A B C

Any Questions?

Motion Part 3: Velocity and Acceleration

Speed is the distance an object travels in a specific amount of time. Review: Speed Speed is the distance an object travels in a specific amount of time. To calculate speed: Speed = Distance ÷ Time Distance is in meters (m) Time is in seconds (s) Speed is in meters per second (m/s)

Velocity Sometimes, knowing the speed isn’t enough. For example, sailors must know the speed and direction their boat is travelling in. Velocity is a description of both speed and direction. e.g. a sailboat travelling at 20 kph in a SE direction

Sometimes, knowing the speed isn’t enough. Velocity Sometimes, knowing the speed isn’t enough. For example, sailors must know the speed and direction their boat is travelling in. Velocity is an example of a vector, a quantity that has both magnitude and direction.

Acceleration Acceleration can be: Objects can speed up, slow down or change direction. Acceleration measures how much an object’s speed changes over a certain time. Acceleration can be: A change in speed A change in direction A change in speed & direction

Acceleration can be positive, negative or zero. Positive Acceleration Object speeds up Negative Acceleration Object slows down Zero Acceleration Constant or no speed

Acceleration a = Vfinal - Vinitial t Formula for acceleration: acceleration = change in velocity time a = Vfinal - Vinitial t Velocity: meters per seconds (m/s) Time: seconds (s) Acceleration: meters per second squared (m/s2)

Example 1 a = Vfinal - Vinitial t a = 20.0 m/s - 11.0 m/s 4.0 A motorcycle’s velocity at the top of the hill is 11.0 m/s. 4.0 seconds later it reaches the bottom of the hill with a velocity of 20.0 m/s. What is the acceleration of the motorcycle? a = Vfinal - Vinitial t a = 20.0 m/s - 11.0 m/s 4.0 a = 9.0 m/s 4.0 a = 2.25 m/s2

Example 2 a = Vfinal - Vinitial t - 2.9 m/s2 = 0.0 m/s - 13.0 m/s t A speed skater just finished a race. After she crossed the finish line, she coasted to a complete stop. If her initial speed was 13.0 m/s and her acceleration was -2.9 m/s2, how long did it take her to stop? a = Vfinal - Vinitial t - 2.9 m/s2 = 0.0 m/s - 13.0 m/s t t (- 2.9) = - 13.0 m/s t = - 13.0 m/s / - 2.9 t = 4.5 s

Any Questions?

Motion Part 4: Speed-Time Graphs

Interpreting a D-T Graph (1) Analysis: Time (s) Distance (m) The distance (m) increasing as time (s) passes The distance gets larger and larger with each second This shows (+) acceleration

Interpreting a D-T Graph (1) Analysis: Time (s) Distance (m) The distance (m) decreasing as time (s) passes The distance gets smaller & smaller with each second This shows (-) acceleration

Interpreting a D-T Graph (3) Analysis: The distance (m) from a reference point is increasing It is increasing at a regular rate This shows (0) acceleration Time (s) Distance (m)

Interpreting a D-T Graph (3) Analysis: The object is moving towards the reference point The object is moving at a constant speed The object is moving slowly Time (s) Distance (m)

Interpreting a S-T Graph (4) Analysis: Time (s) Speed (m/s) The speed (m/s) is constant as time (s) passes The object’s speed is not changing This shows (0) acceleration

Interpreting a S-T Graph (5) Analysis: Time (s) Speed (m/s) The speed (m/s) is increasing as time (s) passes The object speed is changing This shows (+) acceleration

Any Questions?