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The position x reached by a particle in terms of its acceleration a and the elapsed time t in the form ? = ?????, where k is a dimensionless constant. Find m and n through dimensional analysis.

The position x reached by a particle in terms of its acceleration a and the elapsed time t in the form ? = ?????, where k is a dimensionless constant. Find m and n through dimensional analysis.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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5) The position x reached by a particle in terms of its acceleration a and the elapsed time t in the form ? = ?????, where k is a dimensionless constant. Find m and n through dimensional analysis.
5) The position x reached by a particle in terms of its acceleration a and the elapsed time t in the form x = kamtn, where k is a dimensionless constant. Find m and n through dimensional analysis. 6) A road journey takes 5 h 30 min at 90.0 km/h. How much time would be saved by traveling at 100 km/h instead?
Transcribed Image Text:5) The position x reached by a particle in terms of its acceleration a and the elapsed time t in the form x = kamtn, where k is a dimensionless constant. Find m and n through dimensional analysis. 6) A road journey takes 5 h 30 min at 90.0 km/h. How much time would be saved by traveling at 100 km/h instead?
Draw a picture Label which directions are positive (x- and y-), and label relevant quantities on diagram Find a second equation... ...if you're missing a quantity needed to use an equation. Draw up a lan on how to link the equations & quantities Solve for the quantity without using numbers First cancel any quantities that are zero. Use algebra to isolate the quantity you need on one side of the equals sign. Check with dimensional analysis Physics Problem Flow Chart Identify explicitly given values Draw a second picture... ...if you have BEFORE/AFTER situations, force additions, vector component diagrams Find relevant equation(s) One that links the given quantities to the quantity you need to find Sub in numbers on paper Make sure units of each number are correct before you substitute in values into the equations Write all given actual numbers in terms of variables. For previously calculated values, use values before rounding for sig figs Identify required quantity and type of problem Look for keywords like "when", "how far", "how fast", etc. Get type of problem from quantities given/sought Use calculator to find value Use as few presses of the "=" or "ENTER" button as possible. Keep extra sig figs until next step Identify implicitly given values Wording that implies specific values: e.g. "at rest", "comes to a stop", "dropped", "smooth surface", "constant velocity" Calculate/convert easily derived quantities For example, the x- and y- components of velocity/force vectors, or the force of gravity given the mass Write conclusion statement with correct sig figs In plain English with correct units
Transcribed Image Text:Draw a picture Label which directions are positive (x- and y-), and label relevant quantities on diagram Find a second equation... ...if you're missing a quantity needed to use an equation. Draw up a lan on how to link the equations & quantities Solve for the quantity without using numbers First cancel any quantities that are zero. Use algebra to isolate the quantity you need on one side of the equals sign. Check with dimensional analysis Physics Problem Flow Chart Identify explicitly given values Draw a second picture... ...if you have BEFORE/AFTER situations, force additions, vector component diagrams Find relevant equation(s) One that links the given quantities to the quantity you need to find Sub in numbers on paper Make sure units of each number are correct before you substitute in values into the equations Write all given actual numbers in terms of variables. For previously calculated values, use values before rounding for sig figs Identify required quantity and type of problem Look for keywords like "when", "how far", "how fast", etc. Get type of problem from quantities given/sought Use calculator to find value Use as few presses of the "=" or "ENTER" button as possible. Keep extra sig figs until next step Identify implicitly given values Wording that implies specific values: e.g. "at rest", "comes to a stop", "dropped", "smooth surface", "constant velocity" Calculate/convert easily derived quantities For example, the x- and y- components of velocity/force vectors, or the force of gravity given the mass Write conclusion statement with correct sig figs In plain English with correct units
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