Linear MotionConceptual Physics

What is motion?•Easy to recognize, hard to describe•This chapter we use Rates to describe

▫Speed, velocity, and acceleration

•Rate a quantity divided by time•This chapter we will only discuss ‘linear’

motion▫Describing motion▫Motion is relative▫Changing motion▫Graphing motion

Average Speed

• Speed A measure of how fast something is• The rate at which distance is travelled

▫Equation v = d/t v – average speed d– total distance t –time

• measured with a unit of distance divided by a unit of time▫m/s, mph, km/hr▫The word ‘per’ means divided by

• Example 10 m/s▫Means travelling 10 meters every second

• 30 mph … means the object is travelling 30 miles every hour

What’s fast?

•If a baseball travels 60 meters in 2 seconds, what was its average speed?

• (60 m)/2 sec = 30 m/s

•If an airplane travels 3600 miles from NYC to LA in 6 hours what was its average speed?

• 3600 miles / 6 hours = 600 mph

Finding distance when speed is Constant•We simply move our speed equation

(v=d/t) around to solve for ‘d’. When we do this we get

▫d = vt distance = velocity x time

•can ONLY be used when speed is

CONSTANT

Why do we say “average” speed? • Objects in the real world do not always travel at

the same constant speed in the course of one trip

• During a car trip, your car may have had an average speed of 40 mph…▫But travelled at many different speeds at specific

times during this trip…. The speed at a specific time is called Instantaneous Speed

▫A car’s speedometer shows instantaneous speed

• If speed is constant then “instantaneous” and “average” will always be the same▫If speed is not constant it is important to understand

the difference between instantaneous speed and average.

Relative Motion

Relative Motion• All motion is relative to something else• ‘relative to’ means ‘from the perspective of’• Usually motion is relative to the Earth• 2 cars on the highway…

• Each Moving at 50 mph in the same direction relative to the Earth▫Would have a speed of 0 mph relative to each

other▫The would be staying right next to each other,

having no motion with respect to the other car

Another Example• Two cars headed toward each other in

opposite direction one with a speed of 50 mph (relative to Earth) and the other w/ a speed of 60 mph (relative to Earth)

• 50 mph 60 mph• Will the purple car view the green car

moving faster or slower than 50 mph?▫Faster, the green car will view the purple car

approaching much faster than 50 mph, the purple cars speed relative to the the green car is 50 + 60 =110 mph

• This is true b/c whoever the observer is does NOT observe their own motion, in other words everything else is moving but them

Knight Rider Debate??

Catching a football•Motion relative to direction of throw

affects its speed relative to the receiver

Another Example•A boat in a river.

• Boat has speed of 10 mph relative to the water, and the water is flowing w/ a speed relative to the Earth of 15 mph in the same direction

•What is the speed of the boat relative to the Earth?

25 mph…… since the current and boat are going in the same direction the speeds will add

Someone floating in a raft next to the boat would have seen the boat moving at a different speed than someone on the shore

10 mph

15 mph

Distance Chart –

Time (s) Distance (m)

0 0

1 7

2 14

3 21

4 28

What will the distance travelled be at the different times, if the object is moving at a constant 7 m/s?

If you were only given this chart and you were asked to find the speed, how could you do it?

Now fill in the next column for speed given the same informationTime (s) Distance (m) Speed (m/s)

0 0 7

1 7 7

2 14 7

3 21 7

4 28 7

Velocity•Speed in a given direction• Velocity

•Example 50 m/s East• Speed•As can be seen in the above example a

velocity must have a direction

•Direction can also be shown with a “+” or “-”▫Ex. A car moving at +30 mph ran into another

car moving at -25 mph This shows the 2 cars in the collision were

moving in opposite directions

Velocity Continued•Velocity = Displacement/Time

▫Displacement – not same as “distance” ‘Displacement’ describes total length

from starting point to ending point Whereas ‘distance’ describes total length

travelled Incorporates direction… how far it is

displaced… Ex. One lap around a high school track

Distance = 400 m Displacement= 0 m you wound up same

place as you started so there was no displacement

Constant & Changing Velocity•Velocity is CONSTANT as long as its speed

and direction are constant• If either speed OR direction is changing then

velocity is not constant

•So Velocity is constant if…▫Object is at rest (not moving)…….or▫Object is moving in a straight line at a constant

speed

• If car is driving at a constant speed of 30 mph in a circle……. Velocity is NOT constant

Acceleration• IF velocity is changing, an acceleration must be

occurring• The rate at which velocity is changing is

called Acceleration• Acceleration can be found with …

• Acceleration can be positive (speeding up), or it can be negative (slowing down) (aka deceleration)

• If an object is undergoing positive acceleration it will be covering a larger distance per second every second

Note- the symbol ‘Δ’ means ‘change in’

Acceleration Table-Object starting from rest and undergoing an acceleration of 3 m/s2

Time (sec)

Velocity (m/s)

Acceleration (m/s2)

Total Distance Travelled (m)

Distance travelled per sec (m)

0 0 3 0 0

1 3 3 1.5 1.5

2 6 3 6 4.5

3 9 3 13.5 7.5

4 12 3 24 10.5

Another Acceleration Table-Object with an initial velocity of 24 m/s, then undergoing an acceleration of – 4 m/s2

Time (sec)

Velocity (m/s)

Acceleration (m/s2)

Total Distance Travelled (m)

Distance travelled per sec (m)

0 24 -4 0 0

1 20 -4 22 22

2 16 -4 40 18

3 12 -4 54 14

4 8 -4 64 10

5 4 -4 70 6

6 0 -4 72 2

Finding Avg. speed when there is constant acceleration

• During acc. object is at a different speed every instant.. So how can we know the average over some time period?

• 2 ways▫Same as before vavg=(total distance)/ time▫Or …. The midpoint of all the speeds vavg=1/2( vf+vi)

Why the midpt? What is the average of these numbers…1,2,3,4,5 ?? Avg = 3 same as mdpoint b/c numbers increase at

regularly by 1. Much like when there is a constant acceleration.

Sooo… If an object started with a velocity of 0 m/s and had an acceleration of 1 m/s2 for 5 seconds its avg. speed would be 3 m/s

Graphs of motion•Motion can also be depicted very well

using graphs•Two types of graphs

▫Displacement vs. time (D-t) graphs▫Speed vs. time (V-t) graphs

Straight,upward line on D-t graph means

constant velocity

Straight,upward line on a V-t graph means

constant acceleration

Dis

pla

cem

en

t (m

)

D-t graph of constant ‘v’•Distance increases at regular intervals, so

constant speed▫Graph below Increases distance by 5 meters

every sec.•To find speed on a distance time graph, find

Slope

Slope• Tells the rate of increase of the y-value as you move across the x values for any

graph• Slope = rise / run

▫ In other words… how much the graph goes up divided by how much the graph goes across

• Slope tells us properties of the motion being depicted▫ On a position time graph slope = velocity

▫ On a Speed-time graph slope = acceleration

Run = 5

Rise = 25

Rise/run=slope= 25/5 =

5 m/s

If you took slope of smaller sections of

the graph you would get the

same answer since ‘v’ is constant

Displacement-time graph of changing velocity

Time (s)

Distance (m)

0 0

1 8

2 11

3 18

4 15

5 25

What is v for 0-1 sec.?? What is v for 0-2 sec.??What is v for 3-5 sec.?? What is v for 0-5 sec. ??

4 m/s5.5 m/s3.5 m/s5 m/s

Velocity vs. Time graph of constant acceleration

Velocity (m/s)

• Speed-time graph• Slope = rise/run …• Rise =

▫ 16 • Run =

▫ 4• Rise/run =

▫ 4 m/s = acceleration

• Position –time Graph• Slope = rise/run …• Rise =

▫ 50 • Run =

▫ 5• Rise/run =

▫ 10 m/s = speed

Free Fall Acceleration

•As objects fall toward the Earth they are accelerating at a rate of 9.8 m/s2 downward

•We can usually round 9.8 m/s2 to 10 m/s2 •Objects in free fall will gain 10 m/s of

speed for every 1 second it is fallingTime (sec)

Instantaneous Speed (m/s)

Acceleration (m/s2)

0 0 10

1 10 10

2 20 10

3 30 10

4 40 10

Air Resistance• As an object is falling air resistance is acting on

it and slowing it down• The faster the object goes the stronger the air

resistance is• There is a point where a falling object is going

so fast the air resistance becomes so strong that the object can no longer accelerate….. This velocity is called terminal velocity

• Object is still falling, but no longer accelerating• In most problems we ignore any affects of air

resistance• Skydive Attempt• Skydiver• Red Bull Stratos Project

Actual Record From 1960

•Video