Lecture 2: 1D Kinematics - Speed - Velocity - Acceleration
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1. Introduction to 1-Dimensional Motion:
Professor Lewin describes 1D motion of a particle. He talks about average velocity, the importance of "+" and "-" signs, and our free choice of origin.
2. Average Speed vs. Average Velocity:
The two are VERY different. The average velocity can be ZERO, while the average speed is LARGE.
3. Instantaneous Velocity:
Considering the incremental change in position x with time t, we arrive at v=dx/dt. The instantaneous velocity is the derivative of the position with respect to time. Professor Lewin reviews when the velocity is zero, positive and negative; he distinguishes speed from velocity.
4. Measuring the Average Speed of a Bullet:
Professor Lewin shoots a bullet through two wires. The average speed can be calculated from the distance between the wires and the elapsed time. All uncertainties in the measurements are discussed; they have to be taken into account in the final answer.
5. Introducing Average Acceleration:
The average acceleration between time t1 and t2 is the vectorial change in velocity divided by (t2-t1).
6. Instantaneous Acceleration:
The acceleration, dv/dt, is the derivative of the velocity with time. It is the second derivative of the position x with time. Professor Lewin shows how to find the sign of the acceleration from the slope in an x-t plot.
7. Quadratic Equation of Position in Time:
When the position is proportional to the square of the time, the velocity depends linearly on time, and the acceleration is constant.
8. 1D Motion with Constant Acceleration:
Professor Lewin writes down a general quadratic equation for the position as a function of time, and he relates the constants in this equation to the initial conditions at time t=0. The gravitational acceleration is a constant (9.80 m/s^2 in Boston), and it is independent of the mass and shape of a free-falling object, if air drag can be ignored (see Lecture #12). You can use this result to measure g using the free fall time measurements from the falling apples in lecture 1. 9. Strobing an Object in Free Fall: Professor Lewin drops an apple from 3.20 m and takes a polaroid picture of the falling apple which is illuminated by a strobe light. First two light flashes per second, and then ten flashes per second.
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