Speed, acceleration, momentum Motion Speed, acceleration, momentum

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

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

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

More practice 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?

Answer 1. D S T D 800 9 800km ▪ 9hrs = 7200km hr

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

Velocity Speed in a given direction. What is the velocity of a boat that travels from St. Peter to Mankato (10 miles) in 15 minutes?

Answer Speed = distance ÷ time Speed = 10 miles ÷ 15 minutes Speed = 0.67 mi/min 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: D (m) T (sec) 0 0 5 7 10 14 15 21

Distance (m) time (sec)

Was your graph a straight line? 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.

Graph the following on a distance-time graph: D (m) T (s) 0 0 5 1 20 2 45 3 80 4 125 5

Distance (m) 0 1 2 3 4 5 time (sec)

Was your graph a curve? 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 graph. From 0-8 sec, constant speed: (25 m/sec) From 8-12 sec, no motion From 12-16 sec, acceleration From 16-20 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: Average Speed (m/s) Time (sec) ____ 0 to 8 ____ 8 to 12 ____ 12 to 20 25 37.5

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

What do the following speed-time graphs depict?

Acceleration Change in velocity Acceleration = ∆V/ ∆T ∆V Can be change in speed or direction Acceleration = ∆V/ ∆T ∆V a 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?

Answer Acceleration = ∆V/ ∆T a = 26m/s – 10m/s 2 s a = 16m/s 2s a = 8m/s/s or 8m/s2

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 t 20mi/hr/s t 4sec = t 2. yes! Because it’s changing direction! 3. no! It’s not changing speed or direction!

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

Answer: Acceleration = ∆V/ ∆T Acceleration = Vf – Vi t a = 20mi/hr – 60mi/hr 4 s a = -40mi/hr 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 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 300lbs x 5m/s = 1500lb-m/s Momentum of the quarterback is 200lbs x 10m/s = 2000lb-m/s The quarterback has a greater momentum!

Momentum problems 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 B? If car B crashes into car A, what is the total momentum?

Answers: P=mv Car A’s momentum = 30mi/hr x 2000lbs PA = 60,000 mi-lbs/hr east Car B’s momentum = 60mi/hr x 2000lbs PB = 120,000 mi-lbs/hr east Total momentum = PA + PB = 60,000 + 120,000 = 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. What is the momentum of car X? What is the momentum of car Y? If car X crashes into car Y, what is the total momentum?

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