ic_sol_w02d1_1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Class Problem 1: Solution Problem 1 A car is driving at a constant but unknown velocity, v 0 , on a straightaway. A motorcycle is a distance d behind the car. Initially, they are both traveling at the same velocity. The motorcycle starts to pass the car by speeding up at a constant acceleration a . When the motorcyclist is side by side with the car, the motorcycle m stops accelerating and is traveling at twice the velocity of the car. How long does the motorcycle accelerate? What was the initial velocity of the car and motorcycle? How far did the motorcycle travel while accelerating? Express all your answers in terms of the given quantities in the problem. I. Understand – get a conceptual grasp of the problem We assume you’ve recognized the problem is in the domain of kinematics – the quantitative description of motion. What is the problem asking? What are the given conditions and assumptions? What is to be found and how is this determined or constrained by the given conditions? In particular : how many objects are there, is the motion in 1, 2, or 3 dimensions, is the motion relative or is there some logical absolute reference frame? Qualitatively describe the motion (in each coordinate and of each body if there are several). Model: Look for the three most common model motions – either the velocity or the acceleration is constant or the motion is uniform circular. Often these apply only to part of the time (or to only one body) – i.e. might the acceleration be constant but different before and after the rocket engine stops or between the two racing cars? Is the motion an example of uniform circular motion. Advice : Write your own representation of the problem’s stated data: draw a motion diagram (strobe picture), a graph of position or velocity or acceleration vs. time, or a diagram. Make a table of these quantities vs. time if it’s numerical. What are the initial conditions and how do you represent conditions mathematically (e.g. until car A passes car B). A great many problems will involve special motion, perhaps in one or another coordinate: constant velocity, constant acceleration, uniform circular motion, relative motion – learn to recognize these motions. Get the problem into your brain! Question: Describe the strategy you have chosen for solving this problem. You may want to consider the following issues. What does a sketch of the 1
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problem look like? What type of coordinate system will you choose? What information can you deduce from a plot of distance vs. time for both the car and the motorcycle? What conditions must be satisfied when the person just catches up to the streetcar?
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