Presentation Lesson 04 Linear Motion - stemgarage.orgstemgarage.org/Toolbox_Physics/Physics...

SCIENCE – PHYSICSSTEM GARAGE

Linear Motion

Chin-Sung Lin

Relative Motion

Motion is Relative

q  All motion is relative

q  Motion is meaningless unless we specify motion relative to a specific object

q  Each such choice is known as a frame of reference

Relative Motion

Frame of Reference

q  An arbitrary coordinate system with reference to which the position or motion of something is described or physical laws are formulated

Relative Motion

Frame of Reference

q  Two frames of reference moving relative to each other with a constant velocity are completely equivalent, and the same laws of mechanics hold in both

Distance & Displacement

Distance

A distance (d) is a scalar quantity A distance is a numerical description of how far

apart objects are or the initial to the final position of an object

Unit: meter (m)

Distance

Displacement

A displacement (d) is a vector quantity A displacement represents the length and direction

of the shortest distance from the initial to the final position of an object

Its direction is from the initial location to the final location

Unit: meter (m)

Displacement

Speed & Velocity

A speed (v) is a scalar quantity

Distance (d) covered per unit of time (t). Speed is a measure of how fast something is moving. It is the rate at which distance is covered

Unit: meters per second (m/s), miles per hour (mi/h), kilometers per hour (km/h)

Average Speed

Average speed (v):

v = d / t

d = total distance covered (m)

t = time interval (s)

d slope = v

Instantaneous Speed

The speed (v) at any instance of an object is called the instantaneous speed

It is equal to the slope of the tangent line at that moment

d slope = v

Approximation of Instantaneous Speed

Constant Speed

The speed at any instance of an object is constant

slope = vx

slope = 0

Constant Speed

d slope = vx

slope = 0

Constant Speed

d slope = 0

slope = 0

Velocity

A velocity (v) is a vector quantity Velocity is the measurement of the rate and

direction of change in the displacement (d) of an object

v = d / t The speed is the magnitude of velocity

Unit: meters per second (m/s), miles per hour (mi/h), kilometers per hour (km/h)

Speed & Velocity

Speed has only magnitude Velocity has magnitude and direction

Average Velocity

Average velocity (v):

v = d / t

d = total displacement (m)

t = time interval (s)

d slope = v

Instantaneous Velocity

The velocity (v) at any instance of an object is called the instantaneous velocity

It is equal to the slope of the tangent line at that moment

d slope = v

Constant Velocity

To have a constant velocity requires both constant speed and constant direction

Motion at constant velocity is motion in a straight line at constant speed

slope = vx

slope = 0

Constant Velocity

The velocity at any instance of an object is constant

d slope = vx

slope = 0

Constant Velocity

d slope = 0

slope = 0

Constant Velocity

slope = vx

slope = 0

Constant Velocity

slope = vx t

slope = 0

Change Velocity

Either speed or direction (or both) is changing and then the velocity is changing

Change Velocity

Motion at constant speed can have changing velocity all the time when it moves along a curved path

Constant speed

Changing velocity

Change Velocity

Car example:

In a car there are three controls that are used to change the velocity: the gas pedal, the brake and the steering wheel

Acceleration

An acceleration (a) is a vector quantity acceleration is the rate of change of velocity with time

a = Δv / t

a = acceleration (m/s2) Δv = change of velocity (m/s) t = time interval (s)

Acceleration

Acceleration: the slope of the velocity-time (v-t) graph

slope = ax (accelera5on)

Constant Acceleration

The acceleration at any instance of an object is constant. In high school physics. We only deal with constant

acceleration.

slope = ax

slope = 0

The acceleration in the negative direction is also called deceleration. In high school physics, we only deal with constant acceleration.

slope = ax

slope = 0

The acceleration at any instance of an object is constant. Initial velocity is negative.

v slope = ax

slope = 0

Ini5al velocity is nega5ve

velocity is zero

The acceleration in the negative direction is also called deceleration.

Initial velocity is positive.

slope = ax

slope = 0

Ini5al velocity is posi5ve

velocity is zero

Displacement, Velocity & Acceleration

v slope = ax

aslope = 0

d slope = increasing at constant rate

v-t a-t

Displacement, Velocity & Acceleration

slope = ax t

slope = 0

d slope = decreasing at constant rate

v-t a-t

Change Acceleration

Either speed or direction (or both) is changing, i.e., changes in the state of motion, and then the acceleration is changing

The acceleration applies to increases as well as decreases in speed

The decrease in speed is also called deceleration, or negative acceleration

Acceleration An acceleration (a) is also a scalar quantity

When linear (straight-line) motion is considered, it is common to use speed and velocity interchangeably and the acceleration may be expressed as the rate at which speed changes

a = Δv / t

a = acceleration (m/s2) Δv = change of speed (m/s) t = time interval (s)

Acceleration

Car example:

Cars having good acceleration means being able to change velocity quickly and does not necessarily refer to how fast something is moving

Free Fall

When there is no air resistance and the gravity is the only thing affecting a falling object

Elapsed Time

The elapsed time is the time that has elapsed, or passed, since the beginning of the fall

Acceleration due to Gravity

Acceleration due to gravity (g): The free falling object is experiencing acceleration, i.e., a change in speed

The value of acceleration (g) is about 10 m/s2. More accurately, g is 9.81 m/s2

The speed increase 9.81 m/s per second

g is 9.81 m/s2

1 s 5 s

2 s 4 s

v = 30 m/s

v = 20 m/s

v = 10 m/s

v = 0 m/s

v = -‐40 m/s

v = -‐30 m/s

v = -‐20 m/s

v = -‐10 m/s

v = 0 m/s

Constant Accelera5on

g = -‐9.81 m/s2

Velocity Change due to Gravity

slope = g

v-t v = 0

Displacement Change due to Gravity

d slope decreasing at constant rate dy

g = -‐9.81 m/s2

d = dy

Displacement, Velocity & Acceleration due to Gravity

slope = g t

slope = 0

d slope decreasing at constant rate

v-t a-t

slope = g t

slope = 0

d slope decreasing at constant rate

v-t a-t

Constant Direct Propor5on

Quadra5c Parabola

v slope = g

slope = 0

d slope increasing at constant rate

v-t a-t

Slope of v-‐t Area under v-‐t

Instantaneous Velocity in Free Falling

slope = g

t = tf

v = vf

vf = ?

slope = g

t = tf

v = vf

vf = ?

v = gt

vf = gtf

slope = g

t = tf

v = vf

The instantaneous velocity of an object falling from rest:

instantaneous velocity = acceleration x elapsed time

v = gt

slope = g

v-t t = tf

v = vf

When the falling object has initial velocity (vi), whether the object is moving upward or downward, the acceleration due to gravity is always the same (–9.81 m/s2) the entire time

The final velocity (vf), the instantaneous velocity, is:

vf = vi + gt v = vi

slope = g

v-t t = tf

v = vf

vf = vi + gt g = (vf - vi) / t

v = vi

slope = g

v-t t = tf

v = vf

vf = vi + gt g = (vf - vi) / t g = Δv / t

v = vi

Average velocity in Free Falling

slope = g

For any object moving in linear motion with constant acceleration, the average velocity (v) is:

average velocity = (initial velocity + final velocity) / 2

v = vi + vf 2

Displacement-Time Formula Given initial velocity (vi) and time (t), and based on the

formulas we have gotten, find the displacement-time formula

v = vi + vf

vf = vi + gt

v = d / t

Displacement-Time Formula Given initial velocity (vi) and time (t), and based on the

formulas we have gotten, find the displacement-time formula

v = vi + vf

vf = vi + gt

v = d / t

d = vit + ½ gt2

Displacement Change due to Gravity

d Parabola dy

g = -‐9.81 m/s2

d = dy

d = dy + vit + ½ gt2

Distance Change due to Gravity

d Parabola

g = 9.81 m/s2

d = dy

d = vit + ½ gt2

Displacement-Velocity Formula Given initial velocity (vi) and displacement (d), and based

on the formulas we have gotten, find the displacement-velocity formula

d = vit + ½ gt2

g = (vf - vi) / t

Displacement-Velocity Formula Given initial velocity (vi) and displacement (d), and based

on the formulas we have gotten, find the displacement-velocity formula

d = vit + ½ gt2

g = (vf - vi) / t vf

2 = vi2 + 2gd

Summary of Free Falling Formulas

v = vi + vf

vf = vi + gt v = d / t

d = vit + ½ gt2 g = Δv / t

vf2 = vi

2 + 2gd

Summary of Linear Motion Formulas

v = vi + vf

vf = vi + at v = d / t

d = vit + ½ at2 a = Δv / t

vf2 = vi

2 + 2ad

The End

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