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This lecture will help you understand:

Chapter 3 : LINEAR MOTION. This lecture will help you understand:. Motion Is Relative Speed : Average and Instantaneous Velocity Acceleration Free Fall. I recommend writing down items in these yellow boxes. Motion Is Relative.

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This lecture will help you understand:

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  1. Chapter 3: LINEAR MOTION This lecture will help you understand: • Motion Is Relative • Speed : Average and Instantaneous • Velocity • Acceleration • Free Fall I recommend writing down items in these yellow boxes

  2. Motion Is Relative Motion of objects is always described as relative to something else. For example: • You walk on the road relative to Earth, but Earth is moving relative to the Sun. • So your motion relative to the Sun is different from your motion relative to Earth.

  3. Speed (s) • Speed (s) - the distance covered per amount of travel time. • Units are meters per second. (m/s) 6 m 2 s m s d t S = = = 3 m/s Example: A girl runs 6 meters in 2 sec. Her speed is 2 m/s.

  4. Average Speed • The entire distance covered divided by the total travel time • Doesn’t indicate various instantaneous speeds along the way. 200 km 2 h = 100 km/h Example: What is your average speed if you drive a total distance of 200 km in 2 hours?

  5. The average speed of driving 30 km in 1 hour is the same as the average speed of driving 30 km in 1/2 hour. 30 km in 2 hours. 60 km in 1/2 hour. 60 km in 2 hours. Average Speed CHECK YOUR NEIGHBOR

  6. The average speed of driving 30 km in 1 hour is the same as the average speed of driving 30 km in 1/2 hour. 30 km in 2 hours. 60 km in 1/2 hour. 60 km in 2 hours. Average Speed CHECK YOUR ANSWER 60 km 2 hour 30 km 1 hour = Explanation: Average speed = total distance / time So, average speed = 30 km / 1 h = 30 km/h. Same Now, if we drive 60 km in 2 hours: Average speed = 60 km / 2 h = 30 km/h

  7. Instantaneous Speed Instantaneous speed - is the speed at any specific instant. Example: • When you ride in your car, you may speed up and slow down. • Your instantaneous speed is given by your speedometer (your speed at that moment).

  8. d t v = = m/s Δdchange in distance Δt change in time v = = = m/s • Velocity (v) is a description of • the instantaneousspeedof the object • what direction the object is moving (north, left, right, up, down, pos x-axis, neg x-axis) • Vectors have magnitudeand direction • Velocity is a vector quantity. It has • magnitude: instantaneous speed • direction: direction of object’s motion (typically positive and negative x-axis)

  9. Speed (s) and Velocity (v) • Constant speed is steady speed, neither speeding up nor slowing down. • Constant velocityis • constant speed and • constant direction (straight-line path with no acceleration). Motion is relative to Earth, unless otherwise stated.

  10. d t v = = m/s Δdchange in distance Δt change in time v = = = m/s Example: A flying disc leave’s Mr. Pearson’s hand with a velocity of 15 m/s. Ignoring wind resistance, the disc travels for 10 seconds before hitting the ground. How far did the disc travel? no friction = constant velocity Ignoring wind resistance = d t v = 15 m/s v = d = t * v t = 10 s = 10 s * 15m/s d = ____ m d = 150 m

  11. Acceleration Formulated by Galileo based on his experiments with inclined planes.

  12. Acceleration (a) - rate at which velocity changes over time Δvvf - vochange in velocitym/s Δt tf - to change in time s a = = = = = m/s2 vf= velocity final vo= velocity initial (if starting from rest vo = ZERO) tf= time final to= time initial NOTE: Usually we don’t use tf - tojust t = required time vm/s t s a = = = m/s2 vo = velocity at the starting time At time = 0 sec

  13. Example: • You car’s speed right now is 40 km/h. (vo = 40 km/h) • Your car’s speed 2 s later is 45 km/h. (vf = 45 km/h t = 2s ) • Your car’s change in speed is 45 – 40 = 5 km/h. (change = Δv) Δvvf - vochange in velocitym/s Δt t change in time s a = = = = = m/s2 Δvvf - vo45 km/h – 40 km/h5 km/h Δt t 2 s 2 s a = = = = = 2.5 km/h/s Your car’s acceleration is 2.5 km/h/s.

  14. Example: A flying disc leave’s Mr. Pearson’s hand with a velocity of 15 m/s. After 3 seconds, wind resistance slows down the disc to 11 m/s. What is the acceleration of the disc? , Δvvf - vochange in velocitym/s Δt t change in time s a = = = = = m/s2 vm/s t s Change in velocity results in Acceleration a = = = m/s2 vo = 15 m/s 11 m/s – 15 m/s 3 s vf - vo t = a = vf = 11 m/s -4 m/s 3 s t = 3 s a = 1.3 m/s2 = The negative means that the acceleration is in the direction opposite to the motion of the object = resulting in slowing

  15. Example: If a different disc has an acceleration of -2.5 m/s2. What will the velocity be after 2 seconds of flight if Mr. Pearson releases the disc at 13 m/s. Δvvf - vochange in velocitym/s Δt t change in time s a = = = = = m/s2 Don’t wait for the teacher, get to work  vm/s t s a = = = m/s2 vf = 8 m/s Is this answer REASONABLE? Explain x

  16. Acceleration When you are driving a car, what are three things you can do to cause acceleration?. Acceleration involves a change in velocity: • A change in speed (faster or slower), or • A change in direction, or • Both. NOTE: You do not feel velocity You can feel a CHANGE in velocity You DO feel ACCELERATION

  17. An automobile is accelerating when it is slowing down to a stop. rounding a curve at a steady speed. Both of the above. Neither of the above. Acceleration CHECK YOUR NEIGHBOR

  18. An automobile is accelerating when it is slowing down to a stop. rounding a curve at a steady speed. Both of the above. Neither of the above. Acceleration CHECK YOUR ANSWER • Explanation: • Change in speed (increase or decrease) is acceleration, so slowing is acceleration. • Change in direction is acceleration (even if speed stays the same), so rounding a curve is acceleration.

  19. Acceleration and velocity are actually the same. rates but for different quantities. the same when direction is not a factor. the same when an object is freely falling. Acceleration CHECK YOUR NEIGHBOR

  20. Acceleration and velocity are actually the same. rates but for different quantities. the same when direction is not a factor. the same when an object is freely falling. Acceleration CHECK YOUR ANSWER Δdchange in distance Δt change in time v = = = m/s Δvvf - vochange in velocitym/s Δt t change in time s a = = = = = m/s2 • Explanation: • Velocity is the rate at which distance changes over time, • Acceleration is the rate at which velocity changes over time.

  21. Acceleration Galileo increased the inclination of inclined planes. • Steeper inclines gave greater accelerations. • When the incline was vertical, acceleration was max, same as that of the falling object. • When air resistance was negligible, all objects fell with the same unchanging acceleration. Unchanging = CONSTANT Acceleration Which ball hits the ground first? Which ball has the highest vf ? Which ball has the highest vo ?

  22. Free Fall Falling under the influence of gravity only - with no air resistance • Freely falling objects on Earth accelerate at the rate of 10 m/s/s, i.e., 10 m/s2 a = 10 m/s2 = 9.8 m/s2 = 9.81 m/s2 (sig figs) We say this is the acceleration due to gravity (g): a = g = 10 m/s2 = 9.8 m/s2 Text book vs Real World (easier math)

  23. Free Fall—How Fast? The velocity acquired by an object starting from rest is So, under free fall, when acceleration is a = g = 10 m/s2, the speed is v0 = 0 m/s before release: t0 = 0 s v1 = 10 m/s after 1 s t1 = 1 s v2 = 20 m/s after 2 s. t2 = 2 s v3 = 30 m/s after 3 s. t3 = 3 s And so on. Δv t a = Acceleration = Change of 10 m/s per second

  24. Gravity WITH Friction In this situation g still equals 10 m/s2, but the motion of the object is no longer strait down. Here, we must include friction and trigonometry. In this example: a = 4 m/s2NOT 10 m/s2 v0 = 0 m/s before release: t0 = 0 s v1 = 4 m/s after 1 s t1 = 1 s v2 = 8 m/s after 2 s. t2 = 2 s v3 = 12 m/s after 3 s. t3 = 3 s And so on. Δv t a = Acceleration = Change of 4 m/s per second

  25. A free-falling object has a speed of 30 m/s at one instant. Exactly 1 s later its speed will be the same. 35 m/s. more than 35 m/s 60 m/s. Free Fall—How Fast? Δ v = a*t Δv t a = vf = vo +Δv vf = vo + a*t vf = 30m/s +(10m/s2 * 1s) vo = 30 m/s vf = 30m/s +10m/s t = 1 s vf = 40m/s vf = ____ m/s a = g = 10 m/s2  Freely Falling

  26. Free Fall—How Far? The distance covered by an accelerating object -- starting from rest is: d = ½ *a*(t)2 m = ½ *(m/s2)*(s)2 Note that the seconds cancel • So, under free fall, when acceleration is 10 m/s2, the distance is • at t = 1 s; d = ½ *a*(t)2 = ½ (10 m/s2) (1 s)2 = 5 m • at t = 2 s; d = ½ *a*(t)2 = ½ (10 m/s2) (2 s)2 = 20 m • at t = 3 s; d = ½ *a*(t)2 = ½ (10 m/s2) (3 s)2 = 45 m • And so on

  27. What is the distance covered of a freely falling object starting from rest after 4 s? 4 m 16 m 40 m 80 m Free Fall—How Far? CHECK YOUR NEIGHBOR d = ½ *a*(t)2 d = ½ *(10 m/s2)*(4 s)2 d = (5 m/s2) * (16 s2) d = 80 m vo = 0 m/s (rest) t = 4 s d = ____ m  Freely Falling a = g = 10 m/s2

  28. EXAMPLE: A ball thrown straight up into the air begins to slow down (constant acceleration) until it stops in mid air at a height of 34 meters. How long does it take to reach this height? (NOTE: the same equation for free-fall is the same) d = 34 m 2*d = (t)2 a d = ½ *a*(t)2 t = _____ s t = (2*d/a)1/2 a = g = 10 m/s2 Freely Falling t = (2*34 m / 10m/s2)1/2 t = (68 m / 10m/s2)1/2 t = (6.8 s2)1/2 t = 2.6 s  d = 34 m Is this answer REASONABLE?

  29. d t v = = m/s Δdchange in distance Δt change in time d = ½ *a*(t)2 v = = = m/s Free Fall—How Far? at t = 1 s; d = ½ *a*(t)2 = ½ (10 m/s2) (1 s)2 = 5 m at t = 2 s; d = ½ *a*(t)2 = ½ (10 m/s2) (2 s)2 = 20 m Δvvf - vochange in velocitym/s Δt t change in time s a = = = = = m/s2 at t = 2.6 s; d = ½ *a*(t)2 = ½ (10 m/s2) (2.6 s)2 = 34 m at t = 3 s; d = ½ *a*(t)2 = ½ (10 m/s2) (3 s)2 = 45 m d = ½ *a*(t)2 = ½ *(m/s2)*(s)2 = m a = g = 10 m/s2 = 9.8 m/s2 (for freely falling objects)

  30. t3 = 3 s v3 = 0 m/s t2 = 2 s v2 = 10 m/s t4 = 4 s v4 = -10 m/s t4 = 1 s (negative = direction) t1 = 1 s v1 = 20 m/s t5 = 2 s t5 = 5 s v5 = -20 m/s Figure 3.8 t0 = 0 s v0 = 30 m/s Δv t a = t6 = 6 s v6 = -30 m/s t6 = 3 s a = g = 10 m/s2 d = ½ *a*(t)2 vf = vo + a*t t7 = 7 s v7 = -40 m/s t7 = 4 s

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