Use the ideas presented in the text together with your own experience and imagin

Question

Use the ideas presented in the text together with your own experience and imagination to analyze the following questions. Write neatly, and use proper grammar and spelling. Refer to the Homework Guidelines for proper format for your solutions, what you will be graded on, and tips for solving problems. 1 The New Kilogram In 2019, the International Committee for Weights and Measures is expected to adopt a new set of definitions for the fundamental units of the SI system. Instead of a hunk of metal in a safe in Paris, the kilogram will be defined in terms of three other quantities Quantity Symbol Units Transition Frequency of Cesium 133 Atom Aiv Planck's Constant Speed of Light m/S Use dimensional analysis to determine the combination of these three parameters that will define the kilogram. h and c are defined to have exact values. Thus, the measurement that determines the duration of a second will also determine the mass of a kilogram ad the length of a meter! 2 The Least Uncomfortable Journey Some physicists have proposed that the least uncomfortable way to travel a distance D in time T follows a specific mathematical form.T The position s(t) at time t is given by s(t) 3 . A-t2-2.B.t a) The constants A and B are each a combination of the distance D and time T. Use dimensional analysis to determine these combinations. (b) Find the velocity and acceleration as functions of time. BoNus: Suppose you were to travel 100 km in 1 hr according to this trajectory. Use your result from part (a) to determine A and B, then try the following . Make a plot of s(t) What would be your maximum acceleration? (Report your result in symbols and in m/s2.) ISee American Journal of Physics 84, 690 (2016)

Explanation / Answer

Given equation :

s(t) = 3 A t^2 - 2 B t^3

a)Since it is the eqn of position and it has SI unit of meters, So the units of consyant A and B will be:

A - m/s^2

B - m/s^3

b)we know that,

v = ds/dt = s(3 A t^2 - 2 B t^3)/dt = 6 A t - 6 B t^2

Hence, v(t) = 6 A t - 6 B t^2

a = dv/dt = d(6 A t - 6 B t^2)/dt = 6 A - 12 B t

Hence, a(t) = 6A - 12 B t

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