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Punctuality

Class Rules. Punctuality The last person to come into the class later than me will teach the class for 10 minutes Homework to be returned during the first Theory lesson of the week. Cleanliness Courtesy If you need to speak, raise your hands. Consistency

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Punctuality

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  1. Class Rules • Punctuality • The last person to come into the class later than me will teach the class for 10 minutes • Homework to be returned during the first Theory lesson of the week. • Cleanliness • Courtesy • If you need to speak, raise your hands. • Consistency • You must always have your notes with you.

  2. Kinematics Part 5 Equations of Motion

  3. Learning Objectives • By the end of the lesson, you should be able to: • Interpret given examples of non-uniform acceleration. • Solve problems using equations which represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance.

  4. Galileo Galilei and His Experiments Predict-Observe-Explain

  5. The Equations of Motion Recall in the earlier lesson, we have learnt to determine the physical quantities associated with motion graphically. In this lesson, we shall learn how to calculate from the Equations of Motion. Personally, I like to call them, the Equations of Uniform Acceleration because these equations are ONLY APPLICABLE UNDER UNIFORM ACCELERATION!

  6. The Equations of Motion The four equations of motion is given on the left. Each equation caters to finding an unknown physical quantity if three other are known. However, they are often written in the following form, omitting “Δ”. Where s = Δs, that is the change in displacement; t = Δt, that is, the change in time or the time taken; u = initial velocity; v = final velocity; a = acceleration 1 2 3 4

  7. Deriving the Equations of Motion Equation 1. v = u + at (t2, v) v (t1, u) u Velocity/ ms-1 t1 t2 The first equation of motion was derived from the definition of acceleration, given the situation when acceleration is UNIFORM. Time/s

  8. Deriving the Equations of Motion Equation 2. (t2, v) Displacement, s = area under graph = area of trapezium = ½ X (sum of // sides) X ht. = ½ X (u + v) X Δt (t1, u) Velocity/ ms-1 t1 t2 The 2nd equation of motion was derived from determining displacement under the v(t) graph, given the situation when acceleration is UNIFORM. Time/s

  9. Deriving the Equations of Motion Equation 3 and 4.& • Armed with Equation 1 and 2, we may derive Equation 3 and 4. • Can you try deriving Equation 3 and 4? • Are you able to derive a 5th equation of uniform acceleration? What variables will it contain?

  10. Using the Equations of Motion Simple Examples – Direct Application of Equations Optimus Prime accelerates at a rate of 0ms-2 from an initial velocity of 2ms-1 for 10s. What is its velocity at the end of 10s? Meanwhile, Bumblebee accelerates from rest to 10ms-1 in 5s. What is its displacement by the end of the 5s? Megatron tore through the atmosphere at a constant velocity of 400kmh-1 for 5s and then accelerates at 10kmh-2 in the next 3s. What is his displacement during the entire 8s? Starscreamtore through the atmosphere at a constant velocity of 400kmh-1 for 10s. What is his acceleration during this 10s?

  11. Using the Equations of Motion Simple Examples – Direct Application of Equations A ball drops from the top of a building. If the ball takes 4s to impact the ground below, what is the final velocity of the ball before it hits the ground? A ball drops from the top of a building. If the ball took 4s to impact the ground below, what is the height of the building? A ball drops from the top of a building with an initial velocity of 5ms-1. If the ball took 4s to impact the ground below, what is the height of the building? What is the final velocity of the ball from (c), just before impact, if a 1.5m tall (or short) man was standing just below the ball? (Taking acceleration due to gravity, g = 10ms-2) Whose fault is it if the man should get injured (or loses his head)?

  12. Using the Equations of Motion Slightly More Advance Situations • A lunar landing module is descending to the Moon’s surface at a steady velocity of 10ms-1. At a height of 120m, a small object falls from its landing gear. Taking the Moon’s gravitational acceleration as 1.6 ms-1, at what velocity does the object strike the Moon? • The velocity of a car which is decelerating uniformly changes from 30ms-1 to 15ms-1 in 75m. After what distance will it come to rest?

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