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Do Now! Don’t forget there will be a Unit 1 TEST on Friday 25 th September, when Mr Porter will also collect in your folders.

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Last lesson Define displacement, velocity, speed and acceleration Explain the difference between instantaneous and average values of speed, velocity and acceleration

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Displacement Displacement the distance moved in a stated direction (the distance and direction from the starting point). A VECTOR

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Velocity? Velocity is the rate of change of displacement. Also a VECTOR

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An interesting example velocity We have constant speed but changing velocity.

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Acceleration? Acceleration is the rate of change of velocity. Also a VECTOR

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An interesting example velocity We have constant speed but changing velocity. Of course a changing velocity means it must be accelerating!

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Average speed/velocity? Average speed/velocity is change in distance/displacement divided by time taken over a period of time.

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Instantaneous speed/velocity? Instantaneous speed/velocity is the change in distance/displacement divided by time at one particular time.

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Let’s try some questions! Page 45 questions 1, 2, 3, 4, 5, 8, 10.

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Today’s lesson The Equations of Motion (SUVAT)

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The equations of motion The equations of motion can be used when an object is accelerating at a steady rate There are four equations relating five quantities u initial velocity, v final velocity, s displacement, a acceleration, t time SUVAT equations

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The four equations 1This is a re-arrangement of 2This says displacement = average velocity x time 3With zero acceleration, this becomes displacement = velocity x time 4Useful when you don’t know the time NOT in data book

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Beware! All quantities are vectors. These equations are normally done in one dimension, so a negative result means displacement/velocity/acceleration in the opposite direction.

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Example 1 Mr Rayner is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms -1 and his decceleration is 2 ms -2 how long will it take for the car to come to rest?

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Example 1 Mr Rayner is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms -1 and his decceleration is 2 ms -2 how long will it take for the car to come to rest? What does the question tell us. Write it out.

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Example 1 Mr Rayner is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms -1 and his decceleration is 2 ms -2 how long will it take for the car to come to rest? u = 10 ms -1 v = 0 ms -1 a = -2 ms -2 t = ? s

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Example 1 Mr Rayner is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms -1 and his decceleration is 2 ms -2 how long will it take for the car to come to rest? u = 10 ms -1 v = 0 ms -1 a = -2 ms -2 t = ? s Choose the equation that has these quantities in v = u + at

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Example 1 Mr Rayner is driving his car, when suddenly the engine stops working! If he is travelling at 10 ms -1 and his decceleration is 2 ms -2 how long will it take for the car to come to rest? u = 10 ms -1 v = 0 ms -1 a = -2 ms -2 t = ? s v = u + at 0 = 10 + -2t 2t = 10 t = 5 seconds

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Example 2 Jack steps into the road, 30 metres from where Mr Rayner’s engine stops working. Mr Rayner does not see Jack. Will the car stop in time to miss hitting Jack?

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Example 2 Jack steps into the road, 30 metres from where Mr Rayner’s engine stops working. Mr Rayner does not see Jack. Will the car stop in time to miss hitting Jack? What does the question tell us. Write it out.

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Example 2 Jack steps into the road, 30 metres from where Mr Rayner’s engine stops working. Mr Rayner does not see Jack. Will the car stop in time to miss hitting Jack? u = 10 ms -1 v = 0 ms -1 a = -2 ms -2 t = 5 s s = ? m

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Example 2 Jack steps into the road, 30 metres from where Mr Rayner’s engine stops working. Mr Rayner does not see Jack. Will the car stop in time to miss hitting Jack? u = 10 ms -1 v = 0 ms -1 a = -2 ms -2 t = 5 s s = ? m Choose the equation that has these quantities in v 2 = u 2 + 2as

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Example 2 Jack steps into the road, 30 metres from where Mr Rayner’s engine stops working. Mr Rayner does not see Jack. Will the car stop in time to miss hitting Jack? u = 10 ms -1 v = 0 ms -1 a = -2 ms -2 t = 5 s s = ? m v 2 = u 2 + 2as 0 2 = 10 2 + 2x-2s 0 = 100 -4s 4s = 100 s = 25m, the car does not hit Jack.

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1.

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball 12 m.s -1 ?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball 12 m.s -1 ? u = 24 m.s -1 a = -9.8 m.s -2 v = 12 m.s -1 t = ?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball 12 m.s -1 ? u = 24 m.s -1 a = -9.8 m.s -2 v = 12 m.s -1 t = ? v = u + at

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball 12 m.s -1 ? u = 24 m.s -1 a = -9.8 m.s -2 v = 12 m.s -1 v = u + at 12 = 24 + -9.8t -12 = -9.8t t = 12/9.8 = 1.2 seconds

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball -12 m.s -1 ?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball -12 m.s -1 ? u = 24 m.s -1 a = -9.8 m.s -2 v = -12 m.s -1 t = ?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball -12 m.s -1 ? u = 24 m.s -1 a = -9.8 m.s -2 v = -12 m.s -1 v = u + at

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. When is the velocity of the ball -12 m.s -1 ? u = 24 m.s -1 a = -9.8 m.s -2 v = -12 m.s -1 v = u + at -12 = 24 + -9.8t -36 = -9.8t t = 36/9.8 = 3.7 seconds

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the displacement of the ball at those times? (t = 1.2, 3.7)

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the displacement of the ball at those times? (t = 1.2, 3.7) t = 1.2, v = 12, a = -9.8, u = 24 s = ?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the displacement of the ball at those times? (t = 1.2, 3.7) t = 1.2, v = 12, a = -9.8, u = 24 s = ? s = ut + ½at 2 = 24x1.2 + ½x-9.8x1.2 2 s = 28.8 – 7.056 = 21.7 m

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the displacement of the ball at those times? (t = 1.2, 3.7) t = 3.7, v = 12, a = -9.8, u = 24 s = ? s = ut + ½at 2 = 24x3.7 + ½x-9.8x3.7 2 s = 88.8 – 67.081 = 21.7 m (the same?!)

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the velocity of the ball 1.50 s after launch?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the velocity of the ball 1.50 s after launch? u = 24, t = 1.50, a = -9.8, v = ?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the velocity of the ball 1.50 s after launch? u = 24, t = 1.50, a = -9.8, v = ? v = u + at

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the velocity of the ball 1.50 s after launch? u = 24, t = 1.50, a = -9.8, v = ? v = u + at v = 24 + -9.8x1.50 = 9.3 m.s -1

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the maximum height reached by the ball?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the maximum height reached by the ball? u = 24, a = -9.8, v = 0, s = ?

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the maximum height reached by the ball? u = 24, a = -9.8, v = 0, s = ? v 2 = u 2 + 2as 0 = 242 + 2x-9.8xs 0 = 242 -19.6s

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Example 3 A ball is thrown upwards with a velocity of 24 m.s -1. What is the maximum height reached by the ball? u = 24, a = -9.8, v = 0, s = ? 0 = 242 -19.6s 19.6s = 242 s = 242/19.6 = 12.3 m

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Let’s do a shed load of questions Questions 1, 5, 6, 7, 8, 14, 16, 21, 26, 36

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AS-Level Maths: Mechanics 1 for Edexcel

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