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Speed, Velocity, and Acceleration: Interactive Guide

Learn to calculate speed, average speed, velocity, and acceleration with step-by-step examples and practice problems. Understand the magic triangle and how to measure changes in motion with this engaging PowerPoint presentation.

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Speed, Velocity, and Acceleration: Interactive Guide

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  1. Speed, Velocity, and Acceleration An Interactive Power Point

  2. Speed • To calculate speed use the equation: Speed = distance time Speed only gives distance and time

  3. Speed Units • m/s • km/s • m/h • km/h • When you read the first unit, you say meters “PER” second. • Do not write mps

  4. Average Speed • On a trip from Chicago to Texas could you stay the same speed? • You could get an average of all the speeds during the trip.

  5. How do we calculate average speed? • The total distance of the trip divided by the total time of travel.

  6. Magic Triangle • This triangle tells you the formulas you need for speed, distance, and time • s = d t • d = s x t • t = d s

  7. Speed Problems • A baseball moves 11 m in 1 sec. What is its speed? • Speed = distance time • A car travels 70 km in 1.75 h (hours). What is its speed? • S = D T

  8. Speed is Relative! • What does it mean when we say that a car moves at a rate of 80 km/h? • What do we mean that it is relative to? • Unless the problem says something else, the motion that we discuss is ALWAYS relative to Earth.

  9. What is Velocity? • Describes the motionand the direction. • Even if speed remains the same, if the direction changes then the velocity has changed.

  10. Follow the steps to solve an equation. • Problem: You walk 5 meters in 3 seconds. What is your velocity? • Step 1: Write what you know. d = 5 meters t = 3 seconds v = ? • Step 2: Write the formula you will use. v = d / t • Step 3: Put the numbers in for the variables that you know. v = 5 meters 3 seconds • Step 4: Do the math. v = 1.6667meters/seconds = 1.7m/s Your velocity is 1.7 meters per second.

  11. Equations for Speed and Velocity • v = d t • d = v  t • t = d v • You can replace the s(speed) in the triangle for v(velocity)

  12. Calculating Average Speed / Velocity • d= distance • v= speed / velocity • t= time

  13. Sample Speed / Velocity Problems • A car travels a distance of 16 m in 1.8 seconds. What is it’s speed? • d = 16 m • t = 1.8 s • v = ? • v = d t • v = 16m 1.8 s v = 8.89 m/s

  14. Sample Speed / Velocity Problems • Sound travels at a speed of 330 m/s. If a lightning bolt strikes the ground 1 km away from you, how long will it take for the sound to reach you? • v = 330m/s • d = 1km • t = ? • t = d v t = 1km 330m/s You must change the km to m t = 1000m Kids Haven’t Died By Doing Crazy Metric 330m/s t = 3.03 s

  15. Practice Problems • 1.   Calculate the speed of a dog running through a field if he is covering 23.7 meters in 54 seconds. • 2.   If a cross country runner covers a distance of 347 meters in 134 seconds what is her speed? • 3.   What is the speed of a baseball that travels 49 meters in 2.4 seconds?

  16. Practice Problems 4.   What is the speed of a horse in meters per second that runs a distance of 1.2 miles in 2.4 minutes?   • 5.   Calculate the velocity of a car that travels 556 kilometers northeast in 3.4 hours.  Leave your answer in kilometers per hour. • 6.   If the distance covered by a jogger is 2,541meters through the park and the time it took to cover that distance was 43.6 minutes, what was the speed of the jogger?

  17. Practice Problems • 7.   Which object has a greater velocity, a ball rolling down a 3.4 meter hill in six seconds or a fish swimming upstream and covering 5.4 meters in 0.4 minutes? • 8.   If Seneca decides to walk across town to a store that is .95 kilometers away and she has only 25 minutes to get there, what speed does she need to maintain to arrive on time? • 9.   If a projectile flies north 387 meters in 5.8 seconds, what is its velocity? • 10.   Calculate the velocity of a mountain climber if that climber is moving northeast at a pace of 1.6 km in 1.4 hours?  Give your answer in the SI unit for velocity.

  18. Acceleration

  19. What is Acceleration? • The rate of change of velocity. • Car commercial  0 to 60 mph in 10 seconds. • Speeding up • The amount of change of velocity in a time interval.

  20. Acceleration • The rate at which velocity changes • Acceleration is: • Increasing speed • Decreasing speed • Changing direction

  21. How do you measure a change? • The water was at 50m and it rose to 100m. What is the change? • We started at 9:00am and the class was over at 11:00am. What is the change? • The dog grew from 8 lbs to 15 lbs. What is the change? • We had 20 gallons, and now we have 5. What is the change?

  22. Increasing speed • Increase in speed = increase in acceleration • Ex—a car moving from a stopped position

  23. Decreasing speed • Decrease in speed = deceleration (negative acceleration) • Ex– a car decelerates as it stops at a red light

  24. Changing direction • Any change in direction is considered acceleration, even if the object’s speed remains constant • Ex– a Ferris wheel accelerates because it moves in a circle (changes direction). • Its speed is constant

  25. Calculating Acceleration • Calculate the change in velocity during each unit of time • Acceleration = final velocity – initial velocity final time – initial time OR change in velocity (speed) time it took for change

  26. How to Calculate Acceleration? • means “change in”

  27. How do you calculate Δv? • The change in velocity = the final velocity – the initial velocity. Δv = vf – vi • You are stopped at a red light. When it turns green, you speed up to 45m/s. What is your change in velocity? vi = 0m/s vf = 45m/s Δv = ? Δv = vf-vi = 45m/s- 0m/s = 45m/s

  28. Velocity is measured in meters/second • Acceleration is measured in meters per second per second or m/s2 • Acceleration = 22 m/s – 4 m/s 3 s • A= 18 m/s 3 s • A = 6 m/s/s or 6m/s2

  29. Let’s Practice with some Problems • A car’s velocity changes from 0 m/s to 30 m/s in 10 seconds. Calculate the car’s average acceleration. • Acceleration = final velocity – initial velocity change in time • A = 30 m/s – 0 m/s 10s a = 30 m/s 10s a = 3 m/s/s or 3 m/s2

  30. Practice Problem • In 2.5 s a car increases its speed from 60 km/h to 65 km/h while a bicycle goes from rest to 5 km/h. • Which undergoes the greater acceleration? • What is the acceleration of each vehicle?

  31. Answer : A = ending speed – initial speed time interval • Car’s acceleration: • a= 65 km/h – 60 km/h = 5 km/h = 2km/h/s time interval 2.5 s • Bicycle’s acceleration : • A = 5 km/h – 0 km/h = 5km/h = 2 km/h/s 2.5 s 2.5 s

  32. What is negative acceleration? • Also known as DECELERATION. • The negative rate of change of velocity. • Slowing down. • The amount of negative change of velocity in a time interval. • Ex: • 10m/s – 25 m/s = - 15 m/s = - 3m/s/s or – 3m/s2 5 s 5 s

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