**(a)** Suppose that the displacement of an object is related to time according to the expression \( x = Bt^2 \). What are the dimensions of \( B \)?- \( \dfrac{L^2}{L} \)- \(\dfrac{\sqrt{L}}{T} \)- \( L \times T^2 \)- \( \dfrac{T^2}{L} \)- \( \dfrac{L}{T} \)- \( \dfrac{L}{T^2} \)**(b)** A displacement is related to time as \( x = A \sin(2\pi f t) \), where \( A \) and \( f \) are constants. Find the dimensions of \( A \). (\textit{Hint: A trigonometric function appearing in an equation must be dimensionless.})- \( \dfrac{L}{T} \)- \( L \times T \)- \( \dfrac{T}{L} \)- \( L \)- \( T \)

Given data: The expression for the displacement x = Bt2 Required: The dimensions of B

(a) Suppose that the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? O L²/L ✓L T OLX T² O T²/L O L/T O L/T² (b) A displacement is related to time as x = A sin(2лft), where A and fare constants. Find the dimensions of A. (Hint: A trigonometric function appearing in an equation must be dimensionless.) OL/T OLXT O T/L OL OT

(a) Suppose that the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? O L²/L ✓L T OLX T² O T²/L O L/T O L/T² (b) A displacement is related to time as x = A sin(2лft), where A and fare constants. Find the dimensions of A. (Hint: A trigonometric function appearing in an equation must be dimensionless.) OL/T OLXT O T/L OL OT

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)...

See similar textbooks

Similar questions

A rectangle has a length of (5.1 ± 0.2) m and a width of (2.3 ± 0.1) m. Calculate: (a) the area and (b) the perimeter of the rectangle, Give the uncertainty in each value.
Convert the following measurements to metric units with power-of-ten prefixes. Do not use scientific or engineering notation. Numeric values must range from 1 to less than 1000. Metric prefixes, which are case-sensitive, must be one of the following: M, m, c, k, or µ. (You may use lower-case 'u' in place of 'p'.) Example: 2.00 × 105 m = 200 km Enter the numeric value in the first box, and enter the metric prefix in the second box. a. 3.51 x 10-5 L = b. 7.98 x 108 J = C. -0.000230 W = - W d. 11,200 K = K (note: upper-case 'K' is the abbreviation for the temperature unit 'kelvin')
In the equation F= xt +yt?, F = Force and t= time. The dimensions of x and y respectively are O a. MLT-1 & MLTO Ob. MLT1 & MLT2 O. ML-'T & MLTO O d. M°LT-1 & MLT
If the sides of the triangle are given as a= 7 units and b=10 units, what is the longest side of the triangle.
A rectangle has a length of (2.8 ± 0.2) m and a width of (1.7 ± 0.2) m. Calculate the area and the perimeter of the rectangle, and give the uncertainty in each value. (a) Calculate the area and give its uncertainty. (Enter your answers in m2.) m2 ± m2 (b) Calculate the perimeter of the rectangle and give its uncertainty. (Enter your answers in m.) m ± m
A rectangular airstrip measures 32.50 m by 290 m, with the width measured more accurately than the length. Find the area (in m2), taking into account significant figures.
Considering that a drop of water in a rain causes it to fall due to the action of gravity, opposing an air resistance proportional to the square of the velocity, the resulting acceleration would be dV dt = gß – kV² Determine the dimensions of 0 and k, being the.dimensions in . MLT: [V]=[LT'], [t] = [T] e [g] = [LT²].
(a) What Is the area and uncertainty in area of one side of a rectangular plastic brick that has a length of (21.4 + 0.4) cm and a width of (9.8 0.1) cm? (Give your answers in cm².) 209.72 X 6.06 x) cm² (b) What If? If the thickness of the brick is (1.2 ± 0.1) cm, what is the volume of the brick and the uncertainty in this volume? (Give your answers in cm³.) 1.73 X 0.432 x) cm³
Consider the physical quantities s, v, a, m, and t with dimensions [s] = L, [v] = LT-¹, [a] = LT-2, [m] = M, and [t] = T. Select the dimensionally consistent equation(s). U √2as = v S = vtm + a = U S = at at² m
How many significant figures are in the following numbers? (a) 100.0 ± 0.4(b) 4.000 ✕ 106(c) 4.20 ✕ 10-11(d) 0.0060
1.4 Units in equations Given that the following equation calculates position in meters (x) as a function of time in seconds (t): use dimensional analysis to determine the units of the coefficient "u". Xp = Xi + v¡t +,a,t? + 1 2.3/it3+ 2t4/3 2-3 4 2 3.4.54it + 3.7321 · w t3/2 Units of "u" are
1.2 Let us assume that we are to determine the volume of a spherical ball bearing. After of the radius is found to be (9.53± 0.05) mm. (a) What is the volume of then ball bearing? (V="r*) (b) What is the error in volume? (c) How many significant figures should this volume (value) have? (d) Write down the volume in more appropriate units