Chapter 2 and 3 Motion and Accelerated Motion Types of Quantities in Physics Types of Quantities in Physics 1. Scalar- Magnitude(size) examples: speed, volume, temp. mass 2. Vector- magnitude and direction examples: velocity, acceleration, force Resultant- vector representing sum of 2 vectors

Time intervals and Displacement Time Interval- difference between 2 times Time Interval- difference between 2 times   change in a quantity  t= t f -t i  t= t f -t i Displacement- change in position d d d d

Position-Time Graphs Can be used to find the velocity and position of an object Can be used to find the velocity and position of an object

Velocity Speed in a given direction Speed in a given direction What type of quantity is velocity? What type of quantity is velocity? Vector Vector Average Velocity(v)=  d/  t or Average Velocity(v)=  d/  t or d f -d i /t f -t i Instantaneous Velocity- speed and direction at a particular instant example: speedometer 

Determining position with average velocity d=vt + d i or d=vt + d i or d=vt if d i =0 d=vt if d i =0

Ch. 3 Accelerated Motion What is acceleration? What is acceleration? - rate of change of velocity - rate of change of velocity a= v f - v i / t or a=  v /  t - measured in m/s n.html n.html n.html

Types of Acceleration Constant acceleration- velocity changes at a constant rate Constant acceleration- velocity changes at a constant rate Instantaneous acceleration- change in velocity at an instant of time Instantaneous acceleration- change in velocity at an instant of time Deceleration- negative acceleration Deceleration- negative acceleration

Motion with Constant Acceleration A. Final velocity with average acceleration a =  v /  t a  t = v f – v i v f = v i + a  t v f = v i + a  t

Examples(p.65) 18a. A golf ball rolls up a hill toward a miniature-golf hole. Assume that the direction toward the hole is positive. If the golf ball starts with a speed of 2.0 m/s and slows at a constant rate of.50 m/s/s, what is its velocity after 2.0 s? 18a. A golf ball rolls up a hill toward a miniature-golf hole. Assume that the direction toward the hole is positive. If the golf ball starts with a speed of 2.0 m/s and slows at a constant rate of.50 m/s/s, what is its velocity after 2.0 s?

Example(p.65) 20. If a car accelerates from rest at a constant 5.5 m/s/s, how long will it take for the car to reach a velocity of 28 m/s? 20. If a car accelerates from rest at a constant 5.5 m/s/s, how long will it take for the car to reach a velocity of 28 m/s?

B. Position with average acceleration d = v i t + ½ at 2 Example: A car starting from rest is accelerated at 6.1 m/s/s. What is the car’s displacement during the first 7.0 s of acceleration?

What is the difference between displacement and distance? Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion. Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.scalar quantityscalar quantity Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's overall change in position. Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's overall change in position.vector quantityvector quantity To test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. To test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

C. Velocity with Constant Acceleration v f 2 = v i 2 + 2ad Example: A plane is accelerated from a speed of 2.0 m/s at the constant rate of 3.0 m/s/s over a distance of 530 m. What is its speed after traveling this distance?

D. Displacement(Position) during Uniform Acceleration d = ½ ( v f + v i ) t Example: A race car traveling south at 44 m/s is uniformly decelerated to a velocity of 22 m/s over an 11 second interval. What is its displacement during this time?

What is Kinematics? The mathematical description of motion The mathematical description of motion The science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. The science of describing the motion of objects using words, diagrams, numbers, graphs, and equations.

Example(p. 71) 30. A man runs at a velocity of 4.5 m/s for 15.0 min. When going up an increasingly steep hill, he slows down a constant rate of 0.05 m/s/s for 90.0 s and comes to a stop. How far did he run? Hint: This requires two steps.

Example( p. 71) 32. You start your bicycle at the tip of a hill. You coast down the hill at a constant acceleration of 2.00 m/s/s. When you get to the bottom of the hill, you are moving at 18.0 m/s, ad you pedal to maintain that speed. If you continue at this speed for 1.00 min., how far will you have gone from the time you left the hilltop?

Free Fall Free Fall Free Fall –The motion of a body when air resistance is negligible and the motion can be considered due to the force of gravity

Acceleration due to Gravity Acceleration of an object in free fall that results from Earth’s gravity Acceleration of an object in free fall that results from Earth’s gravity Has the symbol “g” Has the symbol “g” g= 9.8 m/s/s ( average value) g= 9.8 m/s/s ( average value) It is a positive number It is a positive number If your coordinate system defines upward to be the positive direction, then acceleration due to gravity is –g and vice versa. If your coordinate system defines upward to be the positive direction, then acceleration due to gravity is –g and vice versa. So in other words a= -g or a=g. So in other words a= -g or a=g.

Examples p A construction worker accidentally drops a brick from a high scaffold. 42. A construction worker accidentally drops a brick from a high scaffold. a.What is the velocity of the brick after 4.0 s? b.How far does the brick fall during this time?

More examples 45. A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caught at the same distance above the ground. 45. A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caught at the same distance above the ground. a. How high does the ball rise? b. How long does the ball remain in the air?