Motion

Some Motion Terms

Distance & DisplacementVelocity & SpeedAccelerationUniform motionScalar .vs. vector

Scalar versus Vector

Scalar - magnitude only (e.g. volume, mass, time)

Vector - magnitude & direction (e.g. weight, velocity, acceleration)

Pictorial Representation

An arrow represents a vector – Length = magnitude of vector– Direction = direction of vector

Pictorial Representation

This arrow could represent a vector of magnitude 10 point to the “right”

This arrow could represent a vector of magnitude 5 point to the “left”

Distance & Displacement

Distance is the actual distance traveled.

Displacement depends only on Start & Finish line

Displacement is the distance traveled , in a certain direction.

Displacement Isn’t Distance

The displacement of an object is not the same as the distance it travels– Example: Throw a ball straight up and then

catch it at the same point you released it The distance is twice the height The displacement is zero


B

A

C

5 m

4 m

3 m

You walk from A to B to C.Your distance traveled is 7mYour displacement form A is 5 m

Velocity & Speed Velocity is the displacement traveled

in a certain time.

Speed is the distance traveled in a certain time.

Velocity is speed in a given direction.

Instantaneous Speed is the speed at any specific instance

Average Speed is the total distance covered divided by total time

Types of Speed

Speed The average speed of an object is

defined as the total distance traveled divided by the total time elapsed

– Speed is a scalar quantity

Average speed total distance

total time

Speed dt

Velocity

The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed

– Velocity is a vector quantity

Average velocity total displacement

total timeV

x t

Speed, cont Average speed totally ignores any

variations in the object’s actual motion during the trip

The total distance and the total time are all that is important

SI units are m/s

Velocity It takes time for an object to undergo a

displacement The average velocity is rate at which

the displacement occurs

generally use a time interval, so let ti = 0

Vaverage xt

x f x it f ti

x f x it

Velocity continued

Direction will be the same as the direction of the displacement (time interval is always positive)– + or - is sufficient

Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.)– Other units may be given in a problem, but

generally will need to be converted to these

Speed vs. Velocity

Cars on both paths have the same average velocity since they had the same displacement in the same time interval

The car on the blue path will have a greater average speed since the distance it traveled is larger

Speed vs. Velocity

You drive from Yakima to Seattle (140 miles away) You stop in Ellensburg for a 2 hr lunch with a

friend. Your total driving time is 2 hours

Average speed 140 miles

2 hour 2 hour

Average speed 140 miles4 hours

35 mph

Uniform Velocity Uniform velocity is constant velocity The instantaneous velocities are always

the same – All the instantaneous velocities will also

equal the average velocity

Velocity Example

150 Km/hr

100 Km/hr

50 Km/hr

How fast is the plane moving in respect to the ground? 100 Km/hr

Wind35 Km/hr

Velocity again


Wind35 Km/hr

Velocity, yet again

How fast is the plane moving in respect to the ground?

100 Km/hr

Wind35 Km/hr

Result

65 Km/hr

Velocity (finally)


50 Km/hrWind

Velocity again (??)


100 Km/hr

50 Km/hrWind

Resultant

a2

b2c2

a2 b2 c2+ =

Velocity - the last time


100 Km/hr

50 Km/hrWind

Resultant

a2

b2c2

a2 b2 c2+ =

R2 = (100)2 + (50)2 R2 = 10,000 + 2500 R2 = 12,500R = 111.8 Km/hr

(Last) Velocity…

Acceleration Change in velocity divided by

the change in time

a Vt

Acceleration

Changing velocity (non-uniform) means an acceleration is present

Acceleration is the rate of change of the velocity

Units are m/s2 (SI), cm/s2 (cgs), and ft/s2 (US Cust)

Average Acceleration

Vector quantity When the sign of the velocity and the

acceleration are the same (either positive or negative), then the speed is increasing

When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing

Instantaneous & Uniform Acceleration

The limit of the average acceleration as the time interval goes to zero

When the instantaneous accelerations are always the same, the acceleration will be uniform– The instantaneous accelerations will all be

equal to the average acceleration

Relationship Between Acceleration & Velocity

Uniform velocity (shown by red arrows maintaining the same size)

Acceleration equals zero

Relationship Between Velocity & Acceleration

Velocity and acceleration are in the same direction

Acceleration is uniform (blue arrows maintain the same length)

Velocity is increasing (red arrows are getting longer)

Positive velocity and positive acceleration

Relationship Between Velocity & Acceleration

Acceleration and velocity are in opposite directions

Acceleration is uniform (blue arrows maintain the same length)

Velocity is decreasing (red arrows are getting shorter)

Velocity is positive and acceleration is negative

Kinematic Equations

Used in situations with uniform acceleration

V f V0 at

V f2 V0

2 2ax

x x0 V0t 12 at

2

Kinematic Equations - Ex #1

A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 seconds. What is the car’s final velocity?

Kinematic Equations - Ex #1 - Ans

A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 seconds. What is the car’s final velocity?

V f V0 at

V f 6ms

2 ms2 6s18m

s


A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 meters. What is the car’s final velocity?


A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 meters. What is the car’s final velocity?

V f2 V0

2 2ax

V f2 6m

s

2

2 2 ms2 6m

V f2 36m

2

s2 24 m2

s2 60m2

s2

V f 60m2

s2 7.746ms


A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 sec. How far does the car travel?


A car traveling with an initial velocity of 6 m/s, accelerates at 2 m/s2, for 6 sec. How far does the car travel?

x xo V0t 12at 2

x 0 6ms

6s 12

2 ms2 6s 2

x 0 36m 36m 72m

Galileo Galilei

1564 - 1642 Galileo formulated

the laws that govern the motion of objects in free fall

Also looked at:– Inclined planes– Relative motion– Thermometers– Pendulum

Free Fall

All objects moving under the influence of gravity only are said to be in free fall– Free fall does not depend on the object’s

original motion All objects falling near the earth’s

surface fall with a constant acceleration The acceleration is called the

acceleration due to gravity, and indicated by g

Acceleration due to Gravity Symbolized by g g = 9.81 m/s2

g is always directed downward– toward the center of the earth

Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances, free fall is constantly accelerated motion

Free Fall – an object dropped

Initial velocity is zero Let up be positive Use the kinematic

equations– Generally use y instead of x

since vertical Acceleration is g = -9.81

m/s2

vo= 0

a = g

Free Fall – an object thrown downward

a = g = -9.81 m/s2

Initial velocity ≠ 0– With upward

being positive, initial velocity will be negative

vo 0

a = g

Free Fall - example

If a rock is dropped from a building, and it takes 18 seconds to reach the ground, how tall is the building?

Free Fall - answer

V0 0ms

V f ??

x ??

a 9.81ms2

t 18sec

•What do we know?

Free Fall - answer

x(t) x0 V

0t 1

2at2

x(t) 0 0 1

2(-9.81

m

s2)(18 sec)2

x(t) 1587.6 meters 0.986 miles

Motion The End

Motion

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