Chapter 2 One-Dimensional Kinematicszuhairusnizam.uitm.edu.my/phy094/03_LectureOutline … · ·...

Copyright © 2010 Pearson Education, Inc.

Chapter 2

One-Dimensional Kinematics


Units of Chapter 2• Position, Distance, and Displacement

• Average Speed and Velocity

• Instantaneous Velocity

• Acceleration

• Motion with Constant Acceleration

• Applications of the Equations of Motion

• Freely Falling Objects


2-1 Position, Distance, and Displacement

Before describing motion, you must set up a coordinate system –define an origin and a positive direction.



The distance is the total length of travel; if you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi.



Displacement is the change in position. If you drive from your house to the grocery store and then to your friend’s house, your displacement is 2.1 mi and the distance you have traveled is 10.7 mi.


2-2 Average Speed and Velocity

The average speed is defined as the distance traveled divided by the time the trip took:

Average speed = distance / elapsed time

Is the average speed of the red car 40.0 mi/h, more than 40.0 mi/h, or less than 40.0 mi/h?



Average velocity = displacement / elapsed time

If you return to your starting point, your average velocity is zero.



Graphical Interpretation of Average Velocity

The same motion, plotted one-dimensionally and as an x-t graph:


2-3 Instantaneous Velocity

Definition:

(2-4)

This means that we evaluate the average velocity over a shorter and shorter period of time; as that time becomes infinitesimally small, we have the instantaneous velocity.


2-3 Instantaneous VelocityThis plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity is tangent to the curve.


2-3 Instantaneous VelocityGraphical Interpretation of Average and Instantaneous Velocity


2-4 Acceleration

Average acceleration:

(2-5)


2-4 AccelerationGraphical Interpretation of Average and Instantaneous Acceleration:


2-4 Acceleration

Acceleration (increasing speed) and deceleration (decreasing speed) should not be confused with the directions of velocity and acceleration:


2-5 Motion with Constant Acceleration

If the acceleration is constant, the velocity changes linearly:

(2-7)

Average velocity:



Average velocity:

(2-9)

Position as a function of time:

(2-10)

(2-11)

Velocity as a function of position:

(2-12)


2-5 Motion with Constant AccelerationThe relationship between position and time follows a characteristic curve.


2-6 Applications of the Equations of MotionHit the Brakes!


2-7 Freely Falling Objects

Free fall is the motion of an object subject only to the influence of gravity. The acceleration due to gravity is a constant, g.



An object falling in air is subject to air resistance (and therefore is not freely falling).



Free fall from rest:


Summary of Chapter 2

• Distance: total length of travel

• Displacement: change in position

• Average speed: distance / time

• Average velocity: displacement / time

• Instantaneous velocity: average velocity measured over an infinitesimally small time


Summary of Chapter 2• Instantaneous acceleration: average acceleration measured over an infinitesimally small time

• Average acceleration: change in velocity divided by change in time

• Deceleration: velocity and acceleration have opposite signs

• Constant acceleration: equations of motion relate position, velocity, acceleration, and time

• Freely falling objects: constant acceleration g = 9.81 m/s2


Chapter 4

Two-Dimensional Kinematics


Units of Chapter 4

• Motion in Two Dimensions

• Projectile Motion: Basic Equations

• Zero Launch Angle

• General Launch Angle

• Projectile Motion: Key Characteristics


4-1 Motion in Two Dimensions

If velocity is constant, motion is along a straight line:


4-1 Motion in Two Dimensions

Motion in the x- and y-directions should be solved separately:


4-2 Projectile Motion: Basic Equations

Assumptions:

• ignore air resistance

• g = 9.81 m/s2, downward

• ignore Earth’s rotation

If y-axis points upward, acceleration in x-direction is zero and acceleration in y-direction is -9.81 m/s2



The acceleration is independent of the direction of the velocity:



These, then, are the basic equations of projectile motion:


4-3 Zero Launch AngleLaunch angle: direction of initial velocity with respect to horizontal


4-3 Zero Launch Angle

In this case, the initial velocity in the y-direction is zero. Here are the equations of motion, with x0 = 0 and y0 = h:


4-3 Zero Launch AngleThis is the trajectory of a projectile launched horizontally:


4-3 Zero Launch AngleEliminating t and solving for y as a function of x:

This has the form y = a + bx2, which is the equation of a parabola.

The landing point can be found by setting y = 0 and solving for x:


4-4 General Launch Angle

In general, v0x = v0 cos θ and v0y = v0 sin θ

This gives the equations of motion:


Solution page 91


4-4 General Launch AngleSnapshots of a trajectory; red dots are at t = 1 s, t = 2 s, and t = 3 s


4-5 Projectile Motion: Key Characteristics

Range: the horizontal distance a projectile travels

If the initial and final elevation are the same:



The range is a maximum when θ = 45°:


Symmetry in projectile motion:



Summary of Chapter 4

• Components of motion in the x- and y-directions can be treated independently

• In projectile motion, the acceleration is –g

• If the launch angle is zero, the initial velocity has only an x-component

• The path followed by a projectile is a parabola

• The range is the horizontal distance the projectile travels

Chapter 2 One-Dimensional Kinematicszuhairusnizam.uitm.edu.my/phy094/03_LectureOutline … · ·...

Documents

Transcript of Chapter 2 One-Dimensional Kinematicszuhairusnizam.uitm.edu.my/phy094/03_LectureOutline … · ·...