Motion Speed, acceleration, momentum

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

What is motion? If you are standing in one place, and your friend walks by you, are you moving relative to your friend? If you are standing in one place, and your friend walks by you, are you moving relative to your friend? Is your friend moving relative to you? Is your friend moving relative to you? Is either of you moving relative to the earth? Is either of you moving relative to the earth?

Answer: You are moving relative to your friend, and your friend is moving relative to you! You are moving relative to your friend, and your friend is moving relative to you! You (the Joker) are not moving relative to the earth, but your friend is. You are both moving relative to the sun! You (the Joker) are not moving relative to the earth, but your friend is. You are both moving relative to the sun! Who is moving relative to the computerscreen?

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.

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?

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

Change your answer to mi/hr! 0.67mi/min x 60min/hr = 40 mi/hr

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 is accelerating A graph that curves on a distance-time graph shows that the object is accelerating

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

Speed-time graphs Using the distance-time graph from the last frame, draw a speed time graph. First fill in the table below: Using the distance-time graph from the last frame, draw a speed time graph. First fill in the table below: Average Speed (m/s) Time (sec) ____0 to 8 ____8 to 12 ____12 to

What does your graph look like? Constant speed will be a horizontal line on a speed time graph. Constant speed will be a horizontal line on a speed time graph. If the speed decreases, the line will slant down. If the speed decreases, the line will slant down. If the speed increases, the line will slant up. If the speed increases, the line will slant up.

What do the following speed-time graphs depict?

Acceleration Change in velocity Change in velocity Can be change in speed or direction Can be change in speed or direction Acceleration = V i – V f Acceleration = V i – V f t

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 = ∆V/ ∆T Acceleration = ∆V/ ∆T a = 26m/s – 10m/s a = 26m/s – 10m/s 2 s a = 16m/s 2s 2s a = 8m/s/s or 8m/s 2

More acceleration problems 1. A car accelerates at a rate of 20mi/hr/s. How long does it take to reach a speed of 80 mi/hr? 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. ∆V 80mi/hr a t20mi/hr/s t 4sec = t 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 = ∆V/ ∆T Acceleration = ∆V/ ∆T 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: Distance-time graph of acceleration

Distance-time graph of deceleration

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!

Inelastic collision

Elastic collision

Two dimensional collision

Momentum problems 2 cars are heading east, car A is traveling 30mi/hr, car B is traveling 60mi/hr. Each car weighs 2000lbs. 2 cars are heading east, car A is traveling 30mi/hr, car B is traveling 60mi/hr. Each car weighs 2000lbs. What 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 is the total momentum? If car B crashes into car A, what is the total momentum?

Answers: P=mv P=mv Car A’s momentum = 30mi/hr x 2000lbs Car A’s momentum = 30mi/hr x 2000lbs P A = 60,000 mi-lbs/hr east P A = 60,000 mi-lbs/hr east Car B’s momentum = 60mi/hr x 2000lbs Car B’s momentum = 60mi/hr x 2000lbs P B = 120,000 mi-lbs/hr east Total momentum = P A + P B Total momentum = P A + P B = 60, ,000 = 60, ,000 = 180,000 mi-lbs/hr east = 180,000 mi-lbs/hr east

Another momentum problem! Car X is traveling 30mi/hr east, car Y is traveling 60mi/hr west. Each car weighs 2000lbs. Car X is traveling 30mi/hr east, car Y is traveling 60mi/hr west. Each car weighs 2000lbs. 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 is the total momentum? If car X crashes into car Y, what is the total momentum?

Answers: P=mv P=mv Car X’s momentum = 30mi/hr x 2000lbs Car X’s momentum = 30mi/hr x 2000lbs P A = 60,000 mi-lbs/hr east P A = 60,000 mi-lbs/hr east Car Y’s momentum = 60mi/hr x 2000lbs Car Y’s momentum = 60mi/hr x 2000lbs P Y = 120,000 mi-lbs/hr west Total momentum = P Y - P X Total momentum = P Y - P X = 120, ,000 = 120, ,000 = 60,000 mi-lbs/hr west = 60,000 mi-lbs/hr west

Which has more momentum?