Accelerated Motion v Chapter 3 Accelerated Motion Nonuniform

Accelerated Motion • v

Chapter 3: Accelerated Motion Nonuniform motion: changing speed or velocity • Uniform motion: constant speed or velocity motion diagram shows changing velocity by: 1. change in spacing of the position of the dots 2. change in length of the velocity vectors

Measuring velocity (in meters per second, m/s) • Velocity interval is defined as: Δ v = vf - vi • The i is initial and the f is final ∆ (Greek letter “delta”) stands for “change in” or final – initial

ACCELERATION • Acceleration is the measure of the change in velocity over a given time. • Constant velocity means no acceleration (or constant acceleration). Dv a = Dt a: average acceleration (m/s 2) v: velocity (m/s) t: time (s)

Velocity-Time graph • Similar to Position. Time graph • Displays the velocity of an object at any time • Slope of the line shows the average acceleration • Ex. - p. 61

EQUATIONS OF MOTION vf = vi + a t 2 x = vi t + 1/2 a t 2 2 vf - v i = 2 a x x = (vf + vi) t/2

vf = vi + a t *If you know an object’s average acceleration during a time interval, you can use it to determine how much the velocity changed during that time. Ex…. A golf ball rolls up a hill toward a mini-golf hole. Assume the direction toward the hole is positive. If the golf ball starts with a speed of 2. 0 m/s and slows at a constant rate of 0. 50 m/s 2, what is the velocity after 2 s? Vf = 1. 0 m/s

X = vi t + ½ 2 at position with average acceleration – an object’s position at a time after the initial time is equal to the sum of its initial position, the product of the initial velocity and the time, and half the product of the acceleration and the square of the time. Ex. #89 from homework

vf – 2 2 vi = 2 ax velocity with constant acceleration – square of the final velocity equals the sum of the square of the initial velocity and twice the product of the acceleration and the displacement since the initial time. Ex. #90 from homework

ACCELERATION BY GRAVITY • The Earth constantly accelerates all objects towards its center • We use the variable g for the acceleration of gravity • g = 9. 8 m/s 2 • a = - g = - 9. 8 m/s 2 (different from book)

EQUATIONS OF MOTION vf = vi - g t 2 y = vi t - 1/2 g t 2 2 vf - vi = - 2 g y Ex #99 from hw

FALLING LAB • Materials: – 6 pennies – stop watch – meter stick – tape • Objective: – determine the acceleration of gravity • Each group will turn a paper into me today.

PROCEDURES • Stack five pennies and tape them together. • Drop the five pennies from 3 different heights. • Measure the distance fallen and the time it took to fall to the ground. • Determine the acceleration of gravity. • Repeat the experiment for the single penny. • Complete the chart on the next slide and answer the questions.

FILL OUT THE CHART 1. Find the percent difference between your answer and the accepted answer. 2. How could you improve your results (at least 2 examples)?

CHAPTER 3 80. 8 m/s 2 81. 33 m/s 82. 6 m/s 2, 0 m/s 2, -2 m/s 2, -4 m/s 2 85. Car B, Car A&C tie 86. 607 m/s, 1. 83 mach 89. 43. 2 m, 43. 2 m 90. 138 m, 550 m 92. 925. 7 m 93. 1. 6 x 103 m 99. -20 m/s, -20 m 100. 7. 3 m/s 102. 5. 9 m, 10. 8 m/s 105. 8 m 107. 280 m/s 2, 29 g 109. 3. 1 x 108 m/s 2, 11 ms (1. 14 x 10 -5 s)

equations for test vf = vi + a t x = vi t + 1/2 a t 2 vf 2 - vi 2 = 2 a x x = (vf + vi) t/2 vf = vi - g t y = vi t - 1/2 g t 2 vf 2 - vi 2 = - 2 g y a = ∆v ∆t g = 9. 8 m/s 2