Ted Talk Rich Eisen runs the 40-yard dash.

Lesson 1: Describing Motion with Words Introduction to the Language of Kinematics Kinematics is the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. Scalars are quantities which are fully described by a magnitude alone. (think of “how much”) Vectors are quantities which are fully described by both a magnitude and a direction. (think of “which way – direction”) Check your understanding….. 5 m 30 m/sec, East 5 mi., North 20 degrees Celsius 256 bytes 4000 Calories

Lesson 1: Describing Motion with Words Introduction to the Language of Kinematics Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

Lesson 1: Describing Motion with Words Speed and Velocity Speed is a scalar quantity which refers to "how fast an object is moving." A fast-moving object has a high speed while a slow-moving object has a low speed. An object with no movement at all has a zero speed. Velocity is a vector quantity which refers to "the rate at which an object changes its position."

Lesson 1: Describing Motion with Words Speed and Average Velocity

Lesson 1: Describing Motion with Words Speed and Average Velocity While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed? In miles/hour and m/s

Lesson 1: Describing Motion with Words Speed and Average Velocity While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed? Now convert to meters/sec

Lesson 1: Describing Motion with Words Instantaneous Speed Instantaneous Speed - speed at any given instant in time. Average Speed - average of all instantaneous speeds; found simply by a distance/time ratio.

A horse canters away from its trainer in a straight line moving 100 A horse canters away from its trainer in a straight line moving 100.0 m away in 16.0 s. It then turns abruptly and gallops halfway back in 4.6. Calculate the average speed and average velocity. A bike travels at a constant speed of 4.0 m/s for 5 s. How far does it go? The round trip distance between Earth and the moon is 350,000km, if the speed of a laser is 3.0 x 108 m/s. How much time does it take the laser to travel from Earth to the moon?

1-Dimensional Kinematics Calculating Acceleration

1-Dimensional Kinematics Direction of the Acceleration Vector Acceleration is a vector quantity so it will always have a direction associated with it. The direction of the acceleration vector depends on two factors: whether the object is speeding up or slowing down whether the object is moving in the positive (+) or negative (–) direction The general RULE OF THUMB is: If an object is slowing down, then its acceleration is in the opposite direction of its motion.

1-Dimensional Kinematics Acceleration Observe the animation of the three cars below. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer.

1-Dimensional Kinematics Acceleration

1-Dimensional Kinematics Calculating Acceleration Check Your Understanding Use the equation to determine the acceleration for the two motions below.                                       

4-Motion equations with constant acceleration 1) v= vo + at 2) x = xo + vot + 1 at2 2 3) v2 = vo2 + 2a(x – xo) 4) x = 1 (v + vo)t 2

1. A car starts from rest and accelerates uniformly over a time of 5 1.A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car.

2. An airplane accelerates from rest down a runway at 3 2.An airplane accelerates from rest down a runway at 3.20 m/s2 until it reaches the take off speed of 44.4 m/s Determine the distance traveled before takeoff.

Example 1 Sue Rushin is waiting at a stoplight. When it finally turns green, Sue accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Sue's car during this time period.

Example 2 Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process

Example 3 On a dry road a car with good tires may be able to brake with an acceleration of -4.9 m/s2. How long does such a car, traveling at 25 m/s take to come to rest?

Example 5 A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car.

Last One Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered sled is accelerated to a speed of 444 m/s in 1.8 seconds, what is the distance that the sled travels? And the acceleration?

Describing Motion with Position vs. Time Graphs The position vs. time graphs for the two types of motion – constant velocity and changing velocity (acceleration) – are depicted as follows: + Velocity / Constant Velocity + Velocity / Changing Velocity

Position-Time Graphs We can use a postion-time graph to illustrate the motion of an object. Postion is on the y-axis Time is on the x-axis

Plotting a Distance-Time Graph Axis Distance (position) on y-axis (vertical) Time on x-axis (horizontal) Slope is the velocity Steeper slope = faster No slope (horizontal line) = staying still

1-Dimensional Kinematics Direction of the Acceleration Vector

Where and When We can use a position time graph to tell us where an object is at any moment in time. Where was the car at 4 s? 30 m How long did it take the car to travel 20 m? 3.2 s

Describing in Words

Describing in Words Describe the motion of the object. When is the object moving in the positive direction? Negative direction. When is the object stopped? When is the object moving the fastest? The slowest?

Constant Velocity Objects with a constant velocity have no acceleration This is graphed as a flat line on a velocity time graph.

Velocity-Time Graphs Velocity is placed on the vertical or y-axis. Time is place on the horizontal or x-axis. We can interpret the motion of an object using a velocity-time graph.

Velocity Velocity changes when an object… Speeds Up Slows Down Change direction

Interpret this graph…

Positive and Negative Velocity The first set of graphs show an object traveling in a positive direction. The second set of graphs show an object traveling in a negative direction.

Changing Velocity Objects with a changing velocity are undergoing acceleration. Acceleration is represented on a velocity time graph as a sloped line.

Speeding Up and Slowing Down The graphs on the left represent an object speeding up. The graphs on the right represent an object that is slowing down.

What you get for all test Pencil and calculator A 3 x 5 card that you can write equations on. Constant and conversion sheets The format of all test: 15-20 multiple choice and 5-6 free response.

Displacement from a Velocity-Time Graph The shaded region under a velocity time graph represents the displacement of the object. The method used to find the area under a line on a velocity-time graph depends on whether the section bounded by the line and the axes is a rectangle, a triangle

Area under the curve Find the displacement of the object from 2-5 seconds?

Rank these situations on the magnitude of the displacement during these intervals.

1-Dimensional Kinematics Free Fall and the Acceleration of Gravity A free-falling object is an object which is falling under the sole influence of gravity. Thus, any object which is moving and being acted upon only by the force of gravity is said to be "in a state of free fall." This definition of free fall leads to two important characteristics about a free-falling object: Free-falling objects do not encounter air resistance. All free-falling objects (on Earth) accelerate downwards at a rate of approximately - 9.8 m/s2

Free Fall and the Acceleration of Gravity The Big Misconception "Doesn't a massive object accelerate at a greater rate than a less massive object?"

Galileo Galileo dropped two cannon balls of different weights from the top of Leaning Tower of Piza. The two cannon balls reached the ground at the same time. He proved that when objects of different weights are dropped at the same height and time, they take the same amount of time to fall to the ground (ignoring air resistance).

Remember: g = -10 m/s2 0 m/s - 10 m/s 10 m/s - 20 m/s 20 m/s 30 m/s - 30 m/s Ignoring Air Resistance

Which object hits the ground first? (ignore air friction) Which object hits the ground first when we include air friction?

No Air Resistance With Air Resistance

Free Fall A cell phone drops from a branch in a tree Free Fall A cell phone drops from a branch in a tree. How fast is the cell phone moving after 1.1 sec? b) How far has the cell phone fallen?

Terminal Velocity? a = 0 m/s2 So what is When the force of air resistance becomes large enough to balance the force of gravity, the net force is 0 Newtons — the object stops accelerating. The object is said to have "reached a terminal velocity." a = 0 m/s2

Fun Problems!!!! 1) A penny is dropped from the top of a rollercoaster. The height of the ride is 110m. (neglect air resistance) Find the speed (and the velocity) of the penny when it hits the ground. Find the time it takes for the penny to fall to the ground. Would it be different for a quarter? (how about with air resistance?)

Sign Conventions for Free-Fall A B C D - + Dy v a - - + Up “+” Down “-” -9.8 -9.8 -9.8 -9.8 At point A the change in y is 0, the velocity is positive. At point B the change in y is positive, the velocity is zero. At point C the change in y is 0, the velocity is negative. At point D, the change in y is negative, the velocity is negative. The acceleration for all the points is -9.8 m/s2 Zero Reference Point

2) A stone is thrown straight upward with a speed of 20 m/s. a) How high does it go? b) How long does it take to rise to its maximum height?