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**Motion 11.2 Speed and Velocity**

Chapter 11

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**What are we going to learn?**

Identify types of speed Calculate the speed of an object

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Speed The ratio of the distance an object moves to the amount of time the object moves 2 types: average and instantaneous

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**Average vs. Instantaneous Speed**

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Average Speed Total distance traveled divided by the time it takes to travel that distance Average speed is computed for the entire duration of a trip

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**Formula for average speed is:**

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Instantaneous Speed Rate at which an object is moving at a given moment in time Instantaneous speed is measured at a particular instant

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Speed Graphs The slope of a line on a distance-time graph is speed

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**Velocity Description of both speed and direction of motion**

Velocity is a vector

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**A change in velocity can be the result of a change in speed, a change in direction, or both**

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**Two or more velocities add by vector addition**

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**A boat on a river heads straight across the river**

A boat on a river heads straight across the river. The current is moving parallel to the river banks, so the boat does not land on the bank directly across from the starting location. The resulting motion of the boat is the vector sum of the boat velocity plus the river velocity. The boat starts at Point A and heads towards Point B but reaches the opposite bank of the river at Point C.

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The time required for the boat to cross the river from one side to the other side depends on the boat velocity and the width of the river If the boat velocity is 4 m/s and the river velocity is 3 m/s, the resultant velocity could be determined to be 5 m/s using the Pythagorean Theorem (a2 + b2 = c2)

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**The boat velocity is a, river velocity is b, then the resultant velocity is c**

a = 4 m/s and b = 3 m/s a2 + b2 = c2 = c2 = c2 √¯ 25 = c 5 = c The resultant velocity is 5 m/s

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The time (t) required for the boat to cross a 60-meter wide river (d) would be dependent upon the boat velocity of 4 m/s (v) If d = v • t then t = d / v so t = d / v = (60 m) / (4 m/s) = 15 seconds It would require 15 seconds to cross the 60-meter wide river

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**Determine the average speed and the average velocity.**

* The teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity.

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**Average Speed To determine average speed: d = 12 meters t = 24 seconds**

average speed = d/t = 12 m/ 24 = 0.50 m/s

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Average Velocity Average velocity is displacement (speed with change in direction)/time v = d / t The displacement is 0 meters Average velocity = 0 m/24 s Average velocity = 0 m/s

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**The skier moves from A to B to C to D.**

Determine the average speed and average velocity of the skier during these 3 minutes.

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**Remember: Add up the distances for speed Add up the displacements for velocity**

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A football coach, Seymour, is pacing back and forth along the sidelines from position A to B to C to D. What is the coach's average speed and average velocity?

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**Questions... Define speed.**

The ratio of the distance an object moves to the amount of time the object moves.

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**The SI units for speed are meters per second (m/s).**

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**How is instantaneous speed different from average speed?**

Average speed: speed is calculated for the entire duration of a trip Instantaneous speed: speed that is measured at a particular instant

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**The equation used for calculating average speed is total distance divided by total time (d/t).**

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True or false? You can determine how fast you were going at the midpoint of a trip by calculating average speed for the entire trip. False, the midpoint speed is an instantaneous speed.

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A student walked 1.5 km in 25 minutes, and then, realizing he was late, ran the remaining 0.5 km in 5 minutes. Calculate his average speed on the way to school. Average speed = (1.5 km km) (25 min + 5 min) = km/min

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**What type of speed does an automobile’s speedometer display?**

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**What type of speed does an automobile’s speedometer display?**

Instantaneous speed

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**The slope of a line on a distance-time graph represents speed.**

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**How do speed and velocity differ?**

Speed: distance and time are factors Velocity: distance, time and direction are factors

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**Circle the letter of each sentence that describes a change in velocity.**

a. A moving object gains speed. b. A moving object changes direction. c. A moving object moves in a straight line at a constant speed. d. A moving object slows down.

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True or false? If a car travels around a gentle curve on a highway at 60 km/h, the velocity does not change. False, it’s direction changes as it goes around the curve.

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**How do velocities combine?**

Sum of vectors in magnitude and direction

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**A river flows at a velocity of 3 km/h relative to the riverbank**

A river flows at a velocity of 3 km/h relative to the riverbank. A boat moves upstream at a velocity of 15 km/h relative to the river. What is the velocity of the boat relative to the riverbank? a. 18 km/h downstream b. 15 km/h upstream c. 12 km/h upstream d. 12 km/h downstream (Remember: 3 km/h downstream + 15 km/h upstream = 12 km/h upstream)

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**A person jogs 4. 0 km in 32 min, then 2. 0 km in 22 min, and finally 1**

A person jogs 4.0 km in 32 min, then 2.0 km in 22 min, and finally 1.0 km in 16 min. What is the jogger’s average speed in km/min? 0.1 km/min (4.0 km km km) (32 min + 22 min + 16 min) = 7.0 km 70 min = 0.1 km/min

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**A train travels 190 km in 3. 0 hr, and then 120 km in 2. 0 hr**

A train travels 190 km in 3.0 hr, and then 120 km in 2.0 hr. What is its average speed? (190 km km) (3.0 hr hr) = 310 km 5.0 hr = 6.2 km/hr

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**A car travels 85 km from point A to point B, then 45 km from B to C**

A car travels 85 km from point A to point B, then 45 km from B to C. The total trip took 1.5 hr. What was the average speed of the car? (85 km + 45 km) 1.5 hr = 86.7 km/hr or 87 km/hr

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**A bicyclist travels for 1. 5 hr at an average speed of 32 km/hr**

A bicyclist travels for 1.5 hr at an average speed of 32 km/hr. How far does the bicyclist travel in that time? Average speed = d/t (solve for d) 32 km/hr = d/1.5hr 32 km/hr x 1.5 hr = d 48 km = d

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Draw and label a line showing the slope of a constant high speed (A), constant low speed (B), and varying speed (C) on the graph below. C A B

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**Does a car’s speedometer show instantaneous speed, average speed, or velocity? Explain.**

Instantaneous speed: it shows the speed at one instant in time not over a whole trip nor does it indicate direction

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Describe an experiment you could perform to determine the average speed of a toy car rolling down an incline. Average speed calculations require distance and time. An experiment would involve timing the car from a starting point to an end point and also measuring the distance between the 2 points.

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**A plane’s average speed between 2 cities is 600 km/h**

A plane’s average speed between 2 cities is 600 km/h. If the trip takes 2.5 hours, how far does the plane fly? Average speed = d/t 600 km/h = d/2.5 h 600 km/h x 2.5 h = d 1500 km = d

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