MotionMotion

Speed, acceleration, Speed, acceleration, momentummomentum

What is motion?What is motion?

Motion is your change in position from Motion is your change in position from one point to another.one point to another.

. .

..

SpeedSpeed

Speed is the rate of Speed is the rate of change of position.change of position.

SpeedSpeed

Speed = Distance ÷ TimeSpeed = Distance ÷ Time

D_ D_

S TS T

Example: A car travels 300km in 6 Example: A car travels 300km in 6 hours. What is the speed of the car?hours. What is the speed of the car?

Answer:Answer:

Speed = distance ÷ timeSpeed = distance ÷ time Speed = 300km ÷ 6 hoursSpeed = 300km ÷ 6 hours Speed = 50km/hrSpeed = 50km/hr

More practiceMore practice

1. How far can a plane travel if it flies 1. How far can a plane travel if it flies 800km/hr for 9 hours?800km/hr for 9 hours?

2. How long does it take a ship to go 500 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr?km if it travels at a speed of 50km/hr?

AnswerAnswer

1. 1. DD SS T T

DD800800 9 9

800km 800km ▪ 9hrs = 7200km ▪ 9hrs = 7200km hrhr

AnswerAnswer

2. 2. DD SS T T 500 500 5050 T T

500km ÷ 500km ÷ 50km50km = 10 hrs = 10 hrs hrhr

VelocityVelocity

Speed in a given direction.Speed in a given direction.

What is the velocity of a boat that What is the velocity of a boat that travels from Sheboygan to travels from Sheboygan to Milwaukee (50 miles) in 60 minutes?Milwaukee (50 miles) in 60 minutes?

AnswerAnswer

Speed = distance ÷ timeSpeed = distance ÷ time Speed = 50 miles ÷ 60 Speed = 50 miles ÷ 60

minutesminutes Speed = 0.83 mi/minSpeed = 0.83 mi/min Velocity = 0.83 mi/min SouthVelocity = 0.83 mi/min South

Distance-time graphsDistance-time graphs

On your paper, graph the following:On your paper, graph the following: D (m)D (m) T (sec) T (sec)

00 00 55 77 1010 14 14 1515 21 21

Was your graph a straight Was your graph a straight line?line?

A A distance-time graphdistance-time graph which which is a is a straight linestraight line indicates indicates constant speedconstant speed..

In constant speed, the object In constant speed, the object does not speed up or slow does not speed up or slow down. down.

Graph the following on a Graph the following on a distance-time graph:distance-time graph:

D (m)D (m) T (s)T (s) 00 00 55 11 2020 224545 338080 44125125 55

0 1 2 3 4 5

Was your graph a curve?Was your graph a curve?

A graph that A graph that curvescurves on a on a distance-time graphdistance-time graph shows shows that the object is that the object is acceleratingaccelerating

Distance-time graphsDistance-time graphs

Describe the motion of the object as Describe the motion of the object as shown in the shown in the

graph.graph.From 0-8 sec, constant speed:(25 m/sec);From 8-12 sec, no motion;From 12-16 sec, increase speed;From 16-20 sec, constant speed

Speed-time graphsSpeed-time graphs

Using the distance-time graph from Using the distance-time graph from the last frame, draw a speed time the last frame, draw a speed time graph. First fill in the table below:graph. First fill in the table below:

Average Speed (m/s)Average Speed (m/s) Time (sec) Time (sec)

________ 0 to 80 to 8

________ 8 to 128 to 12

________ 12 to 2012 to 20

25

0

37.5

What does your graph look What does your graph look like?like?

Constant speedConstant speed will be a will be a horizontal horizontal line on a speed time line on a speed time graph. graph.

If the speed If the speed decreasesdecreases, the line , the line will slant will slant downdown..

If the speed If the speed increasesincreases, the line , the line will slant will slant upup..

What do the following speed-What do the following speed-time graphs depict?time graphs depict?

AccelerationAcceleration

Change in velocityChange in velocity Can be change in speed Can be change in speed oror direction direction Acceleration = vf-vi/ ∆TAcceleration = vf-vi/ ∆T vf-vivf-vi

aa ttVf is final velocityVf is final velocityVi is initial velocityVi is initial velocity

Acceleration problemAcceleration problem

A roller coaster’s A roller coaster’s velocity at the top velocity at the top of a hill is 10m/s. of a hill is 10m/s. Two seconds later it Two seconds later it reaches the bottom reaches the bottom of the hill with a of the hill with a velocity of 26m/s. velocity of 26m/s. What is the What is the acceleration of the acceleration of the roller coaster?roller coaster?

AnswerAnswer

Acceleration = Acceleration = Vf – ViVf – Vi / ∆T/ ∆T a = a = 26m/s – 10m/s26m/s – 10m/s

2 s2 sa = a = 16m/s16m/s

2s2sa = 8m/s/s or 8m/sa = 8m/s/s or 8m/s22

More acceleration problemsMore acceleration problems

1. A car accelerates at a rate of 1. A car accelerates at a rate of 20mi/hr/s. How long does it take to 20mi/hr/s. How long does it take to reach a speed of 80 mi/hr?reach a speed of 80 mi/hr?

2. A car travels at 60 miles per hour 2. A car travels at 60 miles per hour around a curve. Is the car around a curve. Is the car accelerating?accelerating?

3. A car travels in a straight line at 3. A car travels in a straight line at 60mi/hr. Is the car accelerating?60mi/hr. Is the car accelerating?

Answers:Answers:

1. 1. Vf – ViVf – Vi

80mi/hr80mi/hra ta t 20mi/hr/s20mi/hr/s t t

4sec = t4sec = t2. yes! Because it’s changing direction!2. yes! Because it’s changing direction!3. no! It’s not changing speed or 3. no! It’s not changing speed or

direction!direction!

DecelerationDeceleration

Negative accelerationNegative acceleration Example: A car slows from Example: A car slows from

60mi/hr to 20mi/hr in 4 60mi/hr to 20mi/hr in 4 seconds. What is its seconds. What is its acceleration?acceleration?

Answer:Answer:

Acceleration = Acceleration = Vf – ViVf – Vi / ∆T/ ∆T Acceleration = Acceleration = Vf – ViVf – Vi

tt a = a = 20mi/hr – 60mi/hr20mi/hr – 60mi/hr

4 s4 sa = a = -40mi/hr-40mi/hr

4s4sa = -10mi/hr/sa = -10mi/hr/s

Review: Distance-time graph of Review: Distance-time graph of accelerationacceleration

Distance-time graph of Distance-time graph of decelerationdeceleration

Review:Speed-time graph of Review:Speed-time graph of accelerationacceleration

Review: Speed-time graph of Review: Speed-time graph of decelerationdeceleration

Review: Distance-time graph of Review: Distance-time graph of constant speedconstant speed

MomentumMomentum

Momentum = Mass x Momentum = Mass x VelocityVelocity

Which has more Which has more momentum: a 140 kg momentum: a 140 kg football player moving at football player moving at 5m/s or a 90 kg quarterback 5m/s or a 90 kg quarterback moving at 10m/s?moving at 10m/s?

Answer:Answer:

Momentum of the 300lb player isMomentum of the 300lb player is140 kg x 5 m/s = 700 kg*m/s140 kg x 5 m/s = 700 kg*m/s

Momentum of the quarterback isMomentum of the quarterback is 90 kg x 10 m/s = 900 kg*m/s90 kg x 10 m/s = 900 kg*m/s

The quarterback has a greater The quarterback has a greater momentum!momentum!

Inelastic collisionInelastic collision

Elastic collisionElastic collision

Two dimensional Two dimensional collisioncollision

Momentum problemsMomentum problems

2 cars are heading east, car A is 2 cars are heading east, car A is traveling 30mi/hr, car B is traveling 30mi/hr, car B is traveling 60mi/hr. Each car has a traveling 60mi/hr. Each car has a mass of 900 kgmass of 900 kgWhat is the momentum of car A?What is the momentum of car A?What is the momentum of car B?What is the momentum of car B? If car B crashes into car A, what If car B crashes into car A, what is the total momentum?is the total momentum?

Answers:Answers: P=mvP=mv Car A’s momentum = 30mi/hr x 900 kgCar A’s momentum = 30mi/hr x 900 kg

PPAA = 27000 kg*mi/hr east = 27000 kg*mi/hr east Car B’s momentum = 60mi/hr x 900 kgCar B’s momentum = 60mi/hr x 900 kg

PPBB = 54000 kg*mi/hr east = 54000 kg*mi/hr east Total momentum = PTotal momentum = PAA + P + PBB

= 27000 + 54000 = 27000 + 54000 = 81000 kg*mi/hr east = 81000 kg*mi/hr east

Another momentum Another momentum problem!problem!

Car X is traveling 30mi/hr east, Car X is traveling 30mi/hr east, car Y is traveling 60mi/hr west. car Y is traveling 60mi/hr west. Each car weighs 900kg.Each car weighs 900kg.What is the momentum of car X?What is the momentum of car X?What is the momentum of car Y?What is the momentum of car Y? If car X crashes into car Y, what If car X crashes into car Y, what is the total momentum?is the total momentum?

Answers:Answers: P=mvP=mv Car X’s momentum = 30mi/hr x 900 kgCar X’s momentum = 30mi/hr x 900 kg

PPAA = 18000kg * mi/hr = 18000kg * mi/hr easteast

Car Y’s momentum = 60mi/hr x 900 kgCar Y’s momentum = 60mi/hr x 900 kg

PPYY = 54000 kg * mi/hr west = 54000 kg * mi/hr west Total momentum = PTotal momentum = PYY - P - PX X

= 54000-18000= 54000-18000 = 36000 kg * mi/hr west= 36000 kg * mi/hr west

Which has more Which has more momentum?momentum?