Motion Speed, velocity Acceleration, & Momentum

Motion An object is in motion when its distance from another object is changing An object is in motion when its distance from another object is changing We use a reference point to determine if an object is in motion We use a reference point to determine if an object is in motion When studying motion, we can calculate speed, velocity, acceleration, & momentum When studying motion, we can calculate speed, velocity, acceleration, & momentum

Frames of Reference Object or point from which motion is determined Object or point from which motion is determined Most common frame Most common frame of reference is the of reference is theEarth Motion is a change Motion is a change in position relative to a frame of reference

Understanding Motion If you are on a ferry boat, how can you determine if it is in motion? If you are on a ferry boat, how can you determine if it is in motion? If the ferry boat is moving, are you in motion? If the ferry boat is moving, are you in motion? Are you in motion relative to the people around you? (the people are the Reference point.) Are you in motion relative to the trees on shore? (the trees are the reference point)

If you are standing still and your friend walks by, who is in motion? Answer: You are moving relative to your friend, and your friend is moving relative to you! You are both in motion. Answer: You are moving relative to your friend, and your friend is moving relative to you! You are both in motion. You are not moving relative to the Earth, but your friend is. You are both moving relative to the sun! It depends on the frame of reference used. You are not moving relative to the Earth, but your friend is. You are both moving relative to the sun! It depends on the frame of reference used.

What is motion? If you and your friend are walking down the hall together at the same speed, in the same direction, are you moving relative to your friend? If you and your friend are walking down the hall together at the same speed, in the same direction, are you moving relative to your friend? Is your friend moving relative Is your friend moving relative to you? Are either of you moving Are either of you moving relative to the Earth?

Answer: You are NOT moving relative to your friend, and your friend is NOT moving relative to you. You both are moving relative to the Earth. You are NOT moving relative to your friend, and your friend is NOT moving relative to you. You both are moving relative to the Earth. When studying motion, the frame of reference must always be considered. When studying motion, the frame of reference must always be considered.

Speed Speed = Distance ÷ Time Speed = Distance ÷ Time D_ D_ S T Example: A car travels 300km in 6 hours. What is the speed of the car?

Answer: Speed = distance ÷ time Speed = distance ÷ time Speed = 300km ÷ 6 hours Speed = 300km ÷ 6 hours Speed = 50km/hr Speed = 50km/hr

More practice 1. How far can a plane travel if it flies 800km/hr for 9 hours? 1. How far can a plane travel if it flies 800km/hr for 9 hours? 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr? 2. How long does it take a ship to go 500 km if it travels at a speed of 50km/hr?

Answer 1. D S T S TD km ▪ 9hrs = 7200km hr hr

Answer 2. D S T S T T 50 T 500km ÷ 50km = 10 hrs hr hr

Velocity Speed in a given direction. Speed in a given direction. What is the velocity of a boat that travels from St. Peter to Mankato (10 miles) in 15 minutes? What is the velocity of a boat that travels from St. Peter to Mankato (10 miles) in 15 minutes? 2 cars are traveling 32 miles per hour, but one is going North, the other is going South. Do they have the same speed? Do they have the same velocity?

Answer Speed = distance ÷ time Speed = distance ÷ time Speed = 10 miles ÷ 15 minutes Speed = 10 miles ÷ 15 minutes Speed = 0.67 mi/min Speed = 0.67 mi/min Velocity = 0.67 mi/min South Velocity = 0.67 mi/min South

What is the difference between speed and velocity? Answer: velocity includes a direction Answer: velocity includes a direction How long does it take an 8 th grader to get from Mrs. McLaren’s classroom door to Mrs. Peterek’s classroom door? How long does it take an 8 th grader to get from Mrs. McLaren’s classroom door to Mrs. Peterek’s classroom door? How would we solve this? How would we solve this?

Answer: 1. We’d need to measure the speed of an average 8 th grader 1. We’d need to measure the speed of an average 8 th grader 2. We’d need to measure the distance from Mrs. McLaren’s door to Mrs. Peterek’s door 2. We’d need to measure the distance from Mrs. McLaren’s door to Mrs. Peterek’s door 3. We’d need to calculate time, when we know the speed and the distance. 3. We’d need to calculate time, when we know the speed and the distance. Time = distance/speed Time = distance/speed

Distance-time graphs On your paper, graph the following: On your paper, graph the following: D (m) T (sec) D (m) T (sec)

Was your graph a straight line? A distance-time graph which is a straight line indicates constant speed. A distance-time graph which is a straight line indicates constant speed. In constant speed, the object does not speed up or slow down. (The acceleration is zero.) In constant speed, the object does not speed up or slow down. (The acceleration is zero.)

Graph the following on a distance- time graph: D (m)T (s) D (m)T (s)

Was your graph a curve? A graph that curves on a distance-time graph shows that the object does not have a constant speed. A graph that curves on a distance-time graph shows that the object does not have a constant speed.

Distance-time graphs Describe the motion of the object as shown in the Describe the motion of the object as shown in the graph. graph. From 0-8 sec, constant speed: (25 m/sec); From 8-12 sec, no motion; From sec, acceleration; From sec, constant speed

Acceleration Acceleration is the rate at which velocity changes Can be change in speed or direction If an object is speeding up, it is said to have a positive acceleration If an object is slowing down, it is said to have a negative acceleration If an object changes direction, but maintains a constant speed, it is still accelerating Acceleration = change in velocity (Vf-Vi) change in time

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

Answer: Acceleration = change in velocity (Vf-Vi) divided by change in time Acceleration = change in velocity (Vf-Vi) divided by change in time a = 26 m/s – 10 m/s a = 26 m/s – 10 m/s 2 s a = 16 m/s 2 s a = 8 m/s/s or 8 m/s 2 Enough of an acceleration to make Matthew’s face look like this:

What do the following speed-time graphs depict?

More acceleration problems 1. A car traveling at 80 mi/hr slows down to 60 mi/hr for a speed limit sign. If it takes them 5 seconds to slow down, what was the car’s acceleration? 2. A car travels at 60 miles per hour around a curve. Is the car accelerating? 3. A car travels in a straight line at 60mi/hr. Is the car accelerating?

Answers: 1. a= vf-vi t a= 80 mi/hr – 60 mi/hr a= 80 mi/hr – 60 mi/hr 5 s 5 s a = 4 mi/hr/s 2. Yes! Because it’s changing direction! 3. No! It’s not changing speed or direction!

Deceleration Negative acceleration Negative acceleration Example: A car slows from 60mi/hr to 20mi/hr in 4 seconds. What is its acceleration? Example: A car slows from 60mi/hr to 20mi/hr in 4 seconds. What is its acceleration?

Answer: Acceleration = change in velocity/change in time Acceleration = change in velocity/change in time Acceleration = Vf – Vi Acceleration = Vf – Vi t a = 20mi/hr – 60mi/hr a = 20mi/hr – 60mi/hr 4 s a = -40mi/hr 4s 4s a = -10mi/hr/s

Review:Speed-time graph of acceleration

Review: Speed-time graph of deceleration

Review: Distance-time graph of constant speed

Momentum Momentum = Mass x Velocity Momentum = Mass x Velocity Which has more momentum: a 300lb football player moving at 5m/s or a 200lb quarterback moving at 10m/s? Which has more momentum: a 300lb football player moving at 5m/s or a 200lb quarterback moving at 10m/s?

Answer: Momentum of the 300lb player is Momentum of the 300lb player is 300lbs x 5m/s = 1500lb-m/s Momentum of the quarterback is Momentum of the quarterback is 200lbs x 10m/s = 2000lb-m/s 200lbs x 10m/s = 2000lb-m/s The quarterback has a greater momentum! The quarterback has a greater momentum!