One Dimensional Motion

Quantity Category 5m 30 m/s, East 5 km, North 20 degrees Celsius 256 bytes 4000 Calories

Distance and Displacement Distance: Scalar quantity. Magnitude of the total displacement between two positions Displacement: Vector quantity. The CHANGE IN POSITION of an object.

Speed: Scalar quantity. Speed and velocity Speed: Scalar quantity. The rate at which an object covers distance. Velocity: Vector quantity. The rate at which an object changes its position.

Examples 1) How long does it take a car traveling at 45km/h to travel 100.0 m? 2) How far does a skateboarder travel in 22 s if his average velocity is 12.0 m/s? 3) A shopping cart moves from a point 3.0 m West of a flagpole to a point 18.0 m East of the flagpole in 2.5 s. Find its average velocity

Average Speed and Average Velocity Instantaneous Speed: Instantaneous Velocity: The speed at any given instant in time The limit of the average velocity as delta t approaches zero.

Displacement-Time Graphs

Displacement-Time Graphs

D-T Graphs Constant velocity: Positive (slow, fast) Constant velocity: Negative (slow, fast) Changing velocity: Positive (slow to fast, fast to slow) Changing velocity: Negative (slow to fast, fast to slow) What is the acceleration like for all of these instances?

Acceleration: The rate at which an object changes its velocity.

EXAMPLES

Examples

Velocity-Time graphs Definitions: line, slope, area under graph

Velocity-Time Graphs

Graphs Positive velocity: (zero acceleration, positive acceleration, negative acceleration) Negative velocity: (positive acceleration, negative acceleration) Ie. Speeding up or slowing down

Time (s) Velocity (m/s) 2 1 3 4 5 6 7 8 10 Exercise: Draw the graph a) What is the acceleration from 0s to 4s? B) From 4s to 8s?

Determine the acceleration of the graph 1. t = 0-1s 2. t= 1-4s 3. t = 4-12s

1. A student starts at their house then walks to the park which is 200 m to the East. They sit at the park and read a book for a few minutes and then remember that they left the oven on, so they run home as fast as they can. Draw a d vs. t graph and a v vs. t graph showing this motion. a. How can you use a d vs. t graph to find the velocity? b. How can you use a v vs. t graph to find the acceleration? c. How can you use a v vs. t graph to find displacement?

3. A student in a car sits at a stop sign at rest for a few seconds, 100 m to the east of Rockridge. Then they drive at a constant speed to the west until they are 100 m west of Rockridge. They reach another stop sign and stop for a few seconds. Draw a d vs. t graph and a v vs. t graph showing their motion.

Examples 1) A sprinter starts from rest and reaches a speed of 12 m/s in 4.25 s. Find his acceleration. 2) A car starts from rest and accelerates at 15 m/s2 for 3.0 s. What is its top speed? 3) If a snowboarder is traveling at 8.0 m/s how long will it take her to reach 36.0 m/s if she can accelerate at a rate of 3.5 m/s2

Free fall A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth).

Free Fall  acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s/s. 

Time (s) Velocity (m/s) 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0

Free-falling objects are in a state of acceleration. Thus, the velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen. 

The Kinematic Equations Describe motion at constant acceleration.

Kinematic Equations

Kinematic Equations Practice 1. A student drops their homework down a wishing well. After 2.4 s it hits the water at the bottom. How deep is the well?

2. A squad car traveling at 7. 0 m/s East speeds up to 22 2. A squad car traveling at 7.0 m/s East speeds up to 22.0 m/s East in 1.7 s. What is its acceleration?

3. A sprinter starts from rest and accelerates uniformly 3. A sprinter starts from rest and accelerates uniformly. He travels 100.0 m south in 9.69 s, what was his acceleration?

4. A banana boat accelerates from 15. 0 km/h at 2. 00 m/s2 4. A banana boat accelerates from 15.0 km/h at 2.00 m/s2. How far has it traveled when it reaches 30.0 km/h?

5. The Rocket Truck is traveling at 16 5. The Rocket Truck is traveling at 16.0 m/s when it is passed by a plane. It immediately hits the jets at accelerates at 14.0m/s2 for 3.25 s. A) What final velocity does it reach? B) How far does it travel in this time? 6. An arrow strikes a can at 32.0 m/s and exits at 31.0 m/s. If the arrow is 42 cm long find its acceleration as it pierced the can. Ignore the width of the can. 7. A BMW and an F1 car both cross the finish line traveling at 200.0 km/h. The BMW comes to a stop in 4.05 s and the F1 in 2.12 s. How much further did the BMW travel while stopping than the F1 car?