Chapter 2 and 3Chapter 2 and 3Motion and Accelerated MotionMotion and Accelerated Motion

Types of Quantities in PhysicsTypes of Quantities in Physics1. Scalar- Magnitude(size)1. Scalar- Magnitude(size)examples: speed, volume, temp. massexamples: speed, volume, temp. mass2. Vector- magnitude and direction2. Vector- magnitude and directionexamples: velocity, acceleration, forceexamples: velocity, acceleration, force

Resultant- vector representing sum of 2 Resultant- vector representing sum of 2 vectorsvectors

Time intervals and DisplacementTime intervals and Displacement

Time Interval- difference between 2 timesTime Interval- difference between 2 times

change in a quantitychange in a quantity

t= tt= tff-t-tii

Displacement- change in positionDisplacement- change in position

dd

Position-Time GraphsPosition-Time Graphs

Can be used to find the velocity and Can be used to find the velocity and position of an objectposition of an object

VelocityVelocity

Speed in a given directionSpeed in a given direction What type of quantity is velocity?What type of quantity is velocity? VectorVector

Average Velocity(v)= Average Velocity(v)= d/ d/ t ort or

ddff-d-dii/t/tff-t-tii

Instantaneous Velocity- speed and direction at a particular Instantaneous Velocity- speed and direction at a particular instantinstantexample: speedometerexample: speedometer

Determining position with Determining position with average velocityaverage velocity

d=vt + dd=vt + di i oror

d=vt if dd=vt if dii =0 =0

Ch. 3Ch. 3Accelerated MotionAccelerated Motion

What is acceleration?What is acceleration? - rate of change of velocity- rate of change of velocity

a= va= vf f - v- vii / t or a= / t or a= v / v / tt

- measured in m/smeasured in m/s22

- http://www.glenbrook.k12.il.us/gbssci/phys/mmedia/kinema/acceln.htmlhttp://www.glenbrook.k12.il.us/gbssci/phys/mmedia/kinema/acceln.html

Types of AccelerationTypes of Acceleration

Constant acceleration- velocity changes at a Constant acceleration- velocity changes at a constant rateconstant rate

Instantaneous acceleration- change in Instantaneous acceleration- change in velocity at an instant of timevelocity at an instant of time

Deceleration- negative accelerationDeceleration- negative acceleration

Motion with Constant Motion with Constant AccelerationAcceleration

A.A. Final velocity with average accelerationFinal velocity with average acceleration

a = a = v / v / tt

a a t = vt = vff – v – vii

vvf = f = vvi + i + a a t t

Examples(p.65)Examples(p.65)

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

Example(p.65)Example(p.65)

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

B. Position with average B. Position with average accelerationacceleration

d = vd = viit + t + ½ at½ at22

Example: A car starting from rest is accelerated Example: A car starting from rest is accelerated at 6.1 m/s/s. What is the car’s displacement at 6.1 m/s/s. What is the car’s displacement during the first 7.0 s of acceleration?during the first 7.0 s of acceleration?

What is the difference between What is the difference between displacement and distance?displacement and distance?

DistanceDistance is a is a scalar quantityscalar quantity which refers to "how which refers to "how much ground an object has covered" during its much ground an object has covered" during its motion. motion.

DisplacementDisplacement is a vector quantity which refers to is a vector quantity which refers to "how far out of place an object is"; it is the object's "how far out of place an object is"; it is the object's overall change in position. overall change in position.

To test your understanding of this distinction, To test your understanding of this distinction, consider the motion depicted in the diagram below. consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.South, 4 meters West, and finally 2 meters North.

C. Velocity with Constant C. Velocity with Constant AccelerationAcceleration

vvff22 = v = vii

22 + 2ad + 2ad

Example: A plane is accelerated from a speed of 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 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 distance of 530 m. What is its speed after traveling this distance?traveling this distance?

D. Displacement(Position) D. Displacement(Position) during Uniform Accelerationduring Uniform Acceleration

d = d = ½ ( v½ ( vff + v + vii) t) t

Example: A race car traveling south at 44 m/s Example: A race car traveling south at 44 m/s is uniformly decelerated to a velocity of 22 is uniformly decelerated to a velocity of 22 m/s over an 11 second interval. What is its m/s over an 11 second interval. What is its displacement during this time?displacement during this time?

What is Kinematics?What is Kinematics?

The mathematical description of motionThe mathematical description of motion

The science of describing the motion of The science of describing the motion of objects using words, diagrams, numbers, objects using words, diagrams, numbers, graphs, and equations. graphs, and equations.

Example(p. 71)Example(p. 71)

30.30. A man runs at a velocity of 4.5 m/s for A man runs at a velocity of 4.5 m/s for 15.0 min. When going up an increasingly 15.0 min. When going up an increasingly steep hill, he slows down a constant rate steep hill, he slows down a constant rate of 0.05 m/s/s for 90.0 s and comes to a of 0.05 m/s/s for 90.0 s and comes to a stop. How far did he run?stop. How far did he run?

Hint: This requires two steps.Hint: This requires two steps.

Example( p. 71)Example( p. 71)

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

Free FallFree Fall

Free FallFree Fall– The motion of a body when air resistance is The motion of a body when air resistance is

negligible and the motion can be considered negligible and the motion can be considered due to the force of gravitydue to the force of gravity

Acceleration due to GravityAcceleration due to Gravity

Acceleration of an object in free fall that results Acceleration of an object in free fall that results from Earth’s gravityfrom 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 numberIt is a positive number If your coordinate system defines upward to be the If your coordinate system defines upward to be the

positive direction, then acceleration due to gravity positive direction, then acceleration due to gravity is –g and vice versa.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.74Examples p.74

42. A construction worker accidentally 42. A construction worker accidentally drops a brick from a high scaffold.drops a brick from a high scaffold.

a.a. What is the velocity of the brick after 4.0 s?What is the velocity of the brick after 4.0 s?

b.b. How far does the brick fall during this time?How far does the brick fall during this time?

More examplesMore examples

45. A tennis ball is thrown straight up with 45. A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caught at an initial speed of 22.5 m/s. It is caught at the same distance above the ground.the same distance above the ground.

a. How high does the ball rise?a. How high does the ball rise?

b. How long does the ball remain in the b. How long does the ball remain in the air?air?