Average Speed Mrs. Martinez Sixth Grade

Welcoming Work Review What is Force? What is Force? What is a balanced force? Describe by using arrows to draw a diagram. What is a balanced force? Describe by using arrows to draw a diagram. What is an unbalanced force? Describe by using arrows to draw a diagram. What is an unbalanced force? Describe by using arrows to draw a diagram. Getting your brain gears turning. What is a distance-time graph? What is a distance-time graph? What is Motion? What is Motion? What is the connection between Speed, Distance, and Time? What is the connection between Speed, Distance, and Time?

Forces A force is a push or pull that one body exerts on another. A force can cause the motion of an object to change. There are two types of forces: A force is a push or pull that one body exerts on another. A force can cause the motion of an object to change. There are two types of forces: Balanced force – one in which the net force is zero. Balanced force – one in which the net force is zero. Unbalanced force – one in which the net force has a numerical value. Unbalanced force – one in which the net force has a numerical value.

Forces + 1 force - 1 force Balanced Force Net force = force- 2 force Unbalanced Force Net force = force Unbalanced Force Net force = +2

Turn and Talk What is motion?

What Is Motion? Motion is when an object changes place or position. To properly describe motion, you need to use the following: Motion is when an object changes place or position. To properly describe motion, you need to use the following: Start and end position? Start and end position? Movement relative to what? Movement relative to what? How far did it go? How far did it go? In what direction did it go? In what direction did it go?

Motion Re-Cap When an object changes its position, motion has occurred. When an object changes its position, motion has occurred. –Distance- How far an object has moved. –Displacement- How far an object has moved in relation to its starting point. –Consider direction Example: Two runners travel along the same straight path in a straight line for 500 meters. At the end of the run their distances are the same but their displacements are different. How can this be so?

SPEED Describes how fast an object is moving. Describes how fast an object is moving.

What Is Speed? Speed is the distance an object travels in a certain amount of time (relationship of all 3) Speed is the distance an object travels in a certain amount of time (relationship of all 3) To calculate speed, you use the following formula: To calculate speed, you use the following formula: Speed (s) =Distance(d) Time (t) Time (t)

Speed- Distance an object travels per unit of time Relationships between speed, distance, and time: Speed = Distance/ Time = d/ t  Constant Speed- speed does not change over time  Average Speed- speed of motion when speed is changing Avg Speed = Total Distance/ Total Time  Instantaneous Speed- speed at any given moment in time (speedometer)

The 3 formulas for Speed, Time & Distance: Using your W/B write them down without using your notes. Speed = Distance Time Time = Distance Speed Distance =Speed xTime Remember them from this triangle: D ST Solving for SpeedSolving for TimeSolving for Distance

DON’T REMEMBER HUH? WELL LET’S REFRESH THAT MEMORY!

Turn and Talk: What is the Relationship between speed, distance and time? Speed is the distance an object travels in a certain amount of time Speed is the distance an object travels in a certain amount of time

Average Speed = Total distance Total time

WB Time! Let’s check out your knowledge! Without using your notes answer: Let’s check out your knowledge! Without using your notes answer: What is the formula for finding speed? What is the formula for finding speed? What is the formula for finding time, using distance and speed? What is the formula for finding time, using distance and speed? What is the formula for finding distance using speed and time? What is the formula for finding distance using speed and time?

Try this Mrs. Martinez walks home from her sister’s house everyday. It takes her 4 minutes and her house is 240 meters away.What is her average speed? Mrs. Martinez walks home from her sister’s house everyday. It takes her 4 minutes and her house is 240 meters away.What is her average speed? 240 meters/ 4 minutes = 240 meters/ 4 minutes = 60 meters per minute. 60 meters per minute.

Example Question 1 Jane drives at an average speed of 45 mph on a journey of 135 miles. How long does the journey take? Jane drives at an average speed of 45 mph on a journey of 135 miles. How long does the journey take? To find a time, we need to divide distance by speed. To find a time, we need to divide distance by speed. 135 miles ÷ 45 mph = 3 hours 135 miles ÷ 45 mph = 3 hours

Example Question 2 Chris cycles at an average speed of 8 mph. If he cycles for 6½ hours, how far does he travel? Chris cycles at an average speed of 8 mph. If he cycles for 6½ hours, how far does he travel? To find a distance, we need to multiply speed by time. To find a distance, we need to multiply speed by time. 8 mph × 6.5 hours = 52 miles 8 mph × 6.5 hours = 52 miles

Example Question 3 Nikki has to travel a total of 351 miles. She travels the first 216 miles in 4 hours. (a) What is her average speed for the first part of the journey? Nikki has to travel a total of 351 miles. She travels the first 216 miles in 4 hours. (a) What is her average speed for the first part of the journey? To find average speed, we need to divide distance by time. To find average speed, we need to divide distance by time. 216 miles ÷ 4 hours = 54 mph 216 miles ÷ 4 hours = 54 mph

Her average speed is the same for the whole of her journey. Her average speed is the same for the whole of her journey. (b) How long does the whole journey take? (b) How long does the whole journey take? To find time, we need to divide distance by speed. To find time, we need to divide distance by speed. 351 miles ÷ 54 mph = 6.5 hours 351 miles ÷ 54 mph = 6.5 hours

15 mins = 025 hour So: 3 hours 15 mins = 325 hours 30 mins = 05 hour So: 7 hours 30 mins = 75 hours 45 mins = 075 hour So: 2 hours 45 mins = 275 hours Reminder: How to change minutes into a decimal

D ST First work it out on your paper then show me on your WB. A windsurfer travelled 28 km in 1 hour 45 mins. Calculate his speed. Speed = Distance Time 28 km 175 h = = 16 km/h 1 hour 45 mins Answer: His speed was 16 km / hour

2 hour 30 mins Answer: He travelled 125 km A salesman travelled at an average speed of 50 km/h for 2 hours 30 mins. How far did he travel? D ST Distance = Speed x Time = 50 x 25 = 125 km

Answer: It took 9 hours 15 minutes A train travelled 555 miles at an average speed of 60 mph. How long did the journey take? D ST Time = Distance Speed = = 925 hours= 9 hours 15 mins

Speed Problem Suppose you ran 2 km in 10 min. What is your speed? Suppose you ran 2 km in 10 min. What is your speed? S = 2 km = 0.2 km/min S = 2 km = 0.2 km/min 10 min 10 min

Ways To Calculate Speed Constant speed is when you are traveling at the same rate of speed, such as 55 mph constantly on a highway. Constant speed is when you are traveling at the same rate of speed, such as 55 mph constantly on a highway. Average speed is taking the total distance traveled, and dividing by the total time it takes. Used for calculations that involve changing speed. Average speed is taking the total distance traveled, and dividing by the total time it takes. Used for calculations that involve changing speed. Instantaneous speed is the speed at any one given point in time. Instantaneous speed is the speed at any one given point in time.

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Practice Question 1 Jim travels 45 miles at 15 mph. How long does it take him? Jim travels 45 miles at 15 mph. How long does it take him?

45 miles/15 mph= 45 miles/15 mph= 3 hrs. 3 hrs.

Practice Question 2 Jemimah walks at 4 mph for 2½ hours. How far does she walk? Jemimah walks at 4 mph for 2½ hours. How far does she walk? She walked 10 miles. She walked 10 miles. 4 mph x 2.5 hrs= 10 miles 4 mph x 2.5 hrs= 10 miles

Practice Question 3 Jenny drives at a constant speed. In the first three hours she travels 81 miles. How far will she have travelled after 5 hours? Jenny drives at a constant speed. In the first three hours she travels 81 miles. How far will she have travelled after 5 hours? She will travel 135 miles She will travel 135 miles 27 mph for 5 hrs= 135 miles 27 mph for 5 hrs= 135 miles

GRAPHING AVERAGE SPEED Using a Distance-Time Graph

Graphing Motion Graph distance on the y- axis and time on the x-axis Graph distance on the y- axis and time on the x-axis Slope = rise = distance = speed run time run time

Graphing Speed Speed is usually graphed using a line graph, and it depicts the distance and time. Speed is usually graphed using a line graph, and it depicts the distance and time. Time is the independent variable, and thus is ALWAYS on the x-axis. Time is the independent variable, and thus is ALWAYS on the x-axis. Distance is the dependent variable, and is ALWAYS on the y- axis. Distance is the dependent variable, and is ALWAYS on the y- axis.

Average Speed What is the AVERAGE speed of the bass boat depicted in the graph? Average Speed = 125 meters = 15.6 m/s 8 seconds

Instantaneous Speed What is the instantaneous speed of the bass boat at t=7 seconds? Instantaneous Speed = 85 meters = 12.1 m/s 7 seconds

Speed Graphs In what time period is the bass boat speeding up? In what time period is the bass boat slowing down? When is the speed NOT changing?

Distance - Time Graph If something is not moving, a horizontal line is drawn. If something is not moving, a horizontal line is drawn. If something starts out slow and then speeds up, its change in speed can look like this. If something starts out slow and then speeds up, its change in speed can look like this.

Learning Checkpoint This graph shows several stages of motion: Stage 1: 100 m in 10 s Stage 2: 50 m in 10 s Stage 3: 150 m in 20 s Calculate the speed as indicated by each of the colors. Calculate the average speed. What is the total distance? What is the displacement?

Solution Stage 1: S= d/ t 100 m/ 10 s= 10 m/s Stage 2: S= d/t 50 m/ 10 s= 5 m/s Stage 3: S= d/t 150 m/ 20 s= 7.5 m/s Avg Speed= Tot d/ Tot t 300 m/ 40 s= 7.5 m/s Distance = 300 meters Displacement = 0 meters

3) At a daily basis, you rotate between classes. Draw a distance vs time graph illustrating the distance you travel during class rotations here at school

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Velocity The speed of an object in a certain direction.

Velocity Velocity is the speed of an object, but the direction is also included. It is calculated the same as speed, but you must include a direction in your answer. Velocity is the speed of an object, but the direction is also included. It is calculated the same as speed, but you must include a direction in your answer. Example: the bass boat was moving 12 mph toward the north. Example: the bass boat was moving 12 mph toward the north.

Velocity V = velocity (meters/second) d = distance (meters) t = time (seconds) V = velocity (meters/second) d = distance (meters) t = time (seconds) d d V = t t speed of an object in a certain direction.

Velocity speed of an object in a certain direction. seconds

Velocity The speed and direction of an object’s motion. The speed and direction of an object’s motion. –88 km / hr southwest

Speed=? Velocity=? Speed=? Velocity=? 16 meters 12 meters 20 meters Total time= 4 seconds Total time= 4 seconds

Acceleration Acceleration is the rate of change of velocity. A change in velocity can be either a change in speed, or direction, or both. Acceleration is the rate of change of velocity. A change in velocity can be either a change in speed, or direction, or both. Deceleration is when acceleration has a negative value. Deceleration is when acceleration has a negative value.

Acceleration The formula for calculating acceleration is: The formula for calculating acceleration is: Acceleration (a) = final velocity (v f ) – initial velocity (v i ) Acceleration (a) = final velocity (v f ) – initial velocity (v i ) time (sec) time (sec) The unit for velocity, in this case, is The unit for velocity, in this case, is m/s/s OR m/s 2 m/s/s OR m/s 2

Acceleration Math Problem A jet starts at rest at the end of a runway and reaches a speed of 80 m/s in 20 s. What is its acceleration? a a = 80 m/s - 0 m/s = 4 m/s s

Acceleration Math Problem A skateboarder is moving in a straight line at a speed of 3 m/s and comes to a stop in 2 sec. What is his acceleration? a a = 0 m/s - 3 m/s = -1.5 m/s2 2 2 m/s

Inertia Inertia is the tendency of an object to resist any change in motion. Put in another way, if an object is moving, it will keep moving until an outside force acts on it. Inertia is the tendency of an object to resist any change in motion. Put in another way, if an object is moving, it will keep moving until an outside force acts on it. Inertia is related to mass: the greater the mass of an object, the greater its inertia. Inertia is related to mass: the greater the mass of an object, the greater its inertia.

Newton’s 1 st Law of Motion Newton’s 1 st Law is also known as the law of inertia. It says: Newton’s 1 st Law is also known as the law of inertia. It says: An object in motion will stay in motion, and an object at rest will stay at rest, unless acted upon by an outside force. An object in motion will stay in motion, and an object at rest will stay at rest, unless acted upon by an outside force. Example: if you are approaching a fence on a running horse, and the horse suddenly stops, you will keep going forward over the horse’s head unless you are wearing a seatbelt! (I don’t care who you are – that’s funny!) Example: if you are approaching a fence on a running horse, and the horse suddenly stops, you will keep going forward over the horse’s head unless you are wearing a seatbelt! (I don’t care who you are – that’s funny!)

Inertia What does a seat belt do for us, in terms of inertia? -it helps us OVERCOME inertia!

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