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Published byRandell Small Modified over 8 years ago
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Forces : Velocity / time graphs and acceleration
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By the end of this presentation, you should be able to: Describe the difference between ‘speed’ and ‘velocity’. Calculate the acceleration of an object. Interpret, plot (or sketch) velocity/time graphs. Use velocity/time graphs to determine the acceleration of an object, or the distance it has travelled.
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Speed vs. Velocity Speed is simply how fast you are travelling… Velocity is “speed in a given direction”… This car is travelling at a speed of 20m/s This car is travelling at a velocity of 20m/s east W Richards Worthing High School
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Acceleration Acceleration = change in velocity (in m/s) (in m/s 2 ) time taken (in s) 1)A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration? 2)A ball is dropped and accelerates downwards at a rate of 10m/s 2 for 12 seconds. How much will the ball’s velocity increase by? 3)A car accelerates from 10 to 20m/s with an acceleration of 2m/s 2. How long did this take? 4)A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration? W Richards Worthing High School
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Answers to question 1 A cyclist accelerates from 0 to 10m/s in 5 seconds. What is her acceleration? Acceleration : a = change in velocity / time taken so a = (10 – 0) / 5 = 10 / 5 = 2m/s 2
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Question 2 A ball is dropped and accelerates downwards at a rate of 10m/s 2 for 12 seconds. How much will the ball’s velocity increase by? Acceleration : a = change in velocity / time taken so 10 = change in velocity / 12 then change in velocity = 10 x 12 = 120m/s
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Question 3 A car accelerates from 10m/s to 20m/s with an acceleration of 2m/s 2. How long did this take? Acceleration : a = change in velocity / time taken so 2 = (20 – 10) / time taken then time taken = (20 – 10) / 2 = 10 / 2 =5s
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Question 4 A rocket accelerates from 1,000m/s to 5,000m/s in 2 seconds. What is its acceleration? Acceleration : a = change in velocity / time taken so a = (5000 – 1000) / 2 then time taken = 4000 / 2 = 2000m/s 2
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Velocity-time graphs 80 60 40 20 0 10 20 30 4050 Velocity m/s t/s
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80 60 40 20 0 1)How fast was the object going after 10 seconds? 2)What is the acceleration from 20 to 30 seconds? 3)What was the deceleration from 30 to 50s? 4)How far did the object travel altogether? 10 20 30 4050 Velocity m/s t/s
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Answers : Question 1 How fast was the object going after 10 seconds? 80 60 40 20 0 10 20 30 40 50 Velocity (m/s) t(s) 40m/s
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Answers : Question 2 What is the acceleration from 20 to 30 seconds? 80 60 40 20 0 10 20 30 40 50 Velocity (m/s) t(s) The acceleration = change in velocity / time taken = (60 – 40) / 10 = 20 / 10 = 2m/s 2
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Answers : Question 3 What was the deceleration from 30 to 50s? 80 60 40 20 0 10 20 30 40 50 Velocity (m/s) t(s) The deceleration = change in velocity / time taken = (60 –0) / 20 = 60 / 20 = 3m/s 2 Have you noticed the gradient of this graph = the acceleration?
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Answers : Question 4 How far did the object travel altogether? 80 60 40 20 0 10 20 30 40 50 Velocity (m/s) t(s) We cannot use distance = speed x time in this case, because the speed is not constant for the whole journey. We can find the answer by calculating the area under the entire graph. First of all, we need to divide the total area into smaller triangles and rectangles and label them. A B C D A = ½ x base x height = ½ x 10 x 40 = 200m B = length x width = 20 x 40 = 800m C = ½ x 10 x 20 = 100m D = ½ x 20 x 60 = 600m The total distance travelled = 1700m
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