1D Kinematics Legacy Problem #19 Guided Solution
Problem*
Cynthia competes in luge competitions during the winter months. She rides solo on a small sled 3 inches off the ground down icy slopes, turning only by use of her feet and the shifting of her weight on the sled. During the initial stage of one downhill luge, Cynthia accelerated from rest at 6.84 m/s/s for 2.39 seconds. Determine the distance she moved during this acceleration phase.
Audio Guided Solution
Physics problems typically begin as word problems and end as mathematical exercises. A good problem solver has effective habits that they naturally use in order to transform that word problem into the math problem. In this problem, what we need to do is carefully read the problem and make an effort to visualize it and to extract information from it that can be used in mathematical equations. So as I read through here about Cynthia on the luge competition, I notice that she starts from rest and accelerates at 6.84 meters per second per second for 2.39 seconds. So as I look at that information, I make an effort to convert the words into symbols and numbers. The first thing I have to notice is she starts from rest, and that's the V original or VO. So I write down VO equals zero meters per second and accelerates at 6.84 meters per second per second. So I write down A equals 6.84 meters per second per second. This acceleration takes place for 2.39 seconds, and that's a time. So I write down T equals 2.39 seconds. Then I ask, like any good problem solver, what is it I'm looking for? I'm looking for the distance, D. D is my unknown. Now taking the time to do this makes the next step very easy. The next step is I have to find an equation and plot the strategy for calculating the unknown. And if I've written down VO equals blah, blah, blah, T equals blah, blah, blah, A equals blah, blah, blah, and D equals question mark, then what I'm going to do is look at my list of equations for an equation that has these four variables in it. And when you scan through that list of equations, you most certainly will find one that goes D equal the original T plus 1 half AT squared. And in that equation, you know three of the four unknown quantities. And any time you have a situation in which you have one equation, one unknown, you know, at least in theory, that you can solve for it. So substitute your known values of VO, A, and T into that equation. The first term on the right side, VOT, drops out because VO is zero. And you're left with D equal 1 half the A value, known, times T squared. T is known. Use your calculator and solve for the unknown and you'll get your answer.
Solution
19.5 m
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(v_o = \units{0}{\unitfrac{m}{s}}\); \(a = \units{4.2}{\unitfrac{m}{s^2}}\); \(v_f = \units{22.9}{\unitfrac{m}{s}}\); \(d = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of 1D Kinematics at The Physics Classroom Tutorial.