Suppose that the displacement of an object is related to time according to the expression x = Bt?. What are the dimensions of B?
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- How does something that operates in milliseconds compare to something that operates in nanoseconds? What is the difference in terms of the order of magnitude?(a) Assume the equation x = At3 + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (b) Determine the dimensions of the derivative dx/dt = 3At2 + B.A map suggests that Atlanta is 730. miles in a direction 5.00°north of east from Dallas. The same map shows that Chicagois 560. miles in a direction 21.0° west of north from Atlanta.Figure P1.68 shows the location of these three cities. Modelingthe Earth as flat, use this information to find the displacementfrom Dallas to Chicago.
- The position of a particle moving along the x axis may be determined from the expression x(t) = btu + ctv, where x will be in meters when t is in seconds. What will be the dimensions of b and c in this case if u = 6 and v = 13? (Use the following as necessary: L for length and T for time.)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.Suppose a machine is invented to measure the amount of knowledge in a student’s head in units called “factoids.” One student is measured at F(t) = t³ − 6t² + 9t factoids at time t, where t is measured in weeks. a. Find the rate at which the student is gaining (or losing) knowledge as a function of time (be sure to give the units). b. During what time between t = 0 and 11 is the student losing knowledge? c. Sketch a graph of the function F(t).
- a) Acceleration is described as space divided by time squared. Determine the dimensions of acceleration and its SI units.b) Kinetic Energy K has dimensions kg m2/s2. It can be written in terms of momentum p and mass m following the equation below. Determine the dimensions of the momentum and its SI units. c) The unit of force is the newton N, where 1 N = 1 kg m/s2. Determine the dimensions and the SI units of the momentum in terms of newtons.d) Newton’s law of universal gravitation is F =Gm1m2/r2 , where F is the magnitude of the gravitational force exerted by one object on another, m1 and m2 are the masses of the objects, and r is the distance between them. Determine the dimensions and the SI units of the proportionality constant G.The following times are given using metric prefixes on the base SI unit of time: the second. Rewrite them in scientific notation without the prefix (in s). For example, 47 Ts would be rewritten as 4.7 ✕ 1013 s. (Enter your answers as m ✕ 10n, where 1 ≤ |m| < 10 and n is an integer.) 984 Ps 986 fs 19 ns 572 µs(a) Suppose that the displacement x of an object is related to time t according to the expression x = Bt2. What are the dimensions of B? T O T/L O L/L O UT O LT? OLXT2 Use L to stand for the dimension of length, and T to stand for the dimension of time, What is the dimension of x? of t? Can you solve the equation for B? (b) Suppose the displacement x of another object is related to time t according to x = A sin(2ft), where A and fare constants. What are the dimensions of A? (Hint:A trigonometric function appearing in an equation must be dimensionless.) O T/L O LUT OL OL x T OT
- Given the quantities a = 4.6 m, b = 4.4 s, c = 75 m/s, what is the value of the quantity d = cb² Number i 0.06 Units m/s^2 ?(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 T OLX T² O T²/L OL/T O L/T² (b) A displacement is related to time as x = A sin(2πft), where A and fare constants. Find the dimensions of A. (Hint: A trigonometric function appearing in an equation must be dimensionless.) OL/T OLX T O T/L OL TConsider the following equations, where x is a position, v is a velocity, a is an acceleration, and t is a time. Using dimension analysis, find what quantity is described by the equation? Options: Position, Velocity, Acceleration, None of the above 1/2 at^2 at x/t x/(t^2)