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General Physics I Lecture 1 Today's Concepts: a) Displacement, Velocity, Acceleration b) 1-D Kinematics with constant acceleration Mechanics Lecture 1, Slide 1 Prelecture Example Mechanics Lecture 1, Slide 4 Prelecture Example Mechanics Lecture 1, Slide 5 Displacement and Velocity in 1-D Displacement Time taken Mechanics Lecture 1, Slide 6 Displacement and Velocity in 1-D The v(t) vs. t plot is just the slope of the x(t) vs. t plot Definition: Speed = |v(t)| Mechanics Lecture 1, Slide 7 Prelecture Question 1 The graph represents the position as a function of time for an object in one-dimensional motion. Identify which statement below correctly identifies the times at which the velocity of the object is greater than zero. A) The velocity is greater than 0 at t = 0 s and t = 4 s. B) The velocity is greater than 0 at t = 2 s. C) The velocity is greater than 0 at t = 0 s and t = 1 s. D) The velocity is greater than 0 at t = 3 s and t = 4 s. E) The velocity is greater than 0 at t = 0, 1, 3, and 4 s. Mechanics Lecture 1, Slide 8 Clicker Question 1 Are the plots shown at the left correctly related A) YES B) NO Mechanics Lecture 1, Slide 9 Clicker Question 2 The velocity vs. time plot of some object is shown to the right. Which diagram below could be the Displacement vs. time plot for the same object? A B C Mechanics Lecture 1, Slide 10 Acceleration Mechanics Lecture 1, Slide 11 Prelecture Question 2 The graph represents the velocity as a function of time for an object in one-dimensional motion. Identify which statement below correctly describes the motion at t = 3 s. A) The object is slowing down and the acceleration is negative. B) The object is speeding up and the acceleration is negative. C) The object is slowing down and the acceleration is positive. D) The object is speeding up and the acceleration is positive. Mechanics Lecture 1, Slide 12 Checkpoint 1 For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time? A A B Mechanics Lecture 1, Slide 13 Constant Acceleration constant a(t) = a Mechanics Lecture 1, Slide 15 Checkpoint 2 At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec? A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet Mechanics Lecture 1, Slide 16 Clicker Question 3 ? 5ft 1ft 9ft 16ft At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec. How far does it move between t = 2 sec and t = 3 sec? A) 1 foot B) 5 feet C) 9 feet D) 16 feet Mechanics Lecture 1, Slide 17 The following questions pertain to the situation described below. Two cars start from rest at a red stop light. When the light turns green, both cars accelerate forward. The blue car accelerates uniformly at a rate of 4.6 m/s2 for 3.6 seconds. It then continues at a constant speed for 7.4 seconds, before applying the brakes such that the carâ€™s speed decreases uniformly coming to rest 195.87 meters from where it started. The yellow car accelerates uniformly for the entire distance, finally catching the blue car just as the blue car comes to a stop. 1. 2. 3. 4. 5. 6. How fast is the blue car going 1.8 seconds after it starts? How fast is the blue car going 7.7 seconds after it starts? How far does the blue car travel before its brakes are applied to slow down? What is the acceleration of the blue car once the brakes are applied? What is the total time the blue car is moving? What is the acceleration of the yellow car? Mechanics Lecture 1, Slide 19