Practice: A box moving with an initial speed **v** is accelerated horizontally. If **x** is measured in [m],**v** in [m/s], **a** in [m/s^{2}], **t** in [s] which of the following equations is correct for solving the distance **x**?

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Introduction to Units | 24 mins | 0 completed | Learn |

Unit Conversions | 17 mins | 0 completed | Learn |

Solving Density Problems | 14 mins | 0 completed | Learn |

Dimensional Analysis | 11 mins | 0 completed | Learn |

Counting Significant Figures | 6 mins | 0 completed | Learn |

Operations with Significant Figures | 11 mins | 0 completed | Learn |

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Uncertainty |

Practice: A box moving with an initial speed **v** is accelerated horizontally. If **x** is measured in [m],**v** in [m/s], **a** in [m/s^{2}], **t** in [s] which of the following equations is correct for solving the distance **x**?

Practice: Newton’s Law of Gravitation describes the attraction force between two masses. The equation is

$\mathit{F}\mathbf{=}\mathit{G}\frac{{\mathit{m}}_{\mathbf{1}}{\mathit{m}}_{\mathbf{2}}}{{\mathit{r}}^{\mathbf{2}}}$

where ** F** is in [

Determine the units of the Universal Constant G.

0 of 3 completed

Answer each question yes or no. Must two quantities have the same dimensions (a) if you are adding them? (b) If you are multiplying them? (c) If you are subtracting them? (d) If you are dividing them? (e) If you are equating them?

What are the dimensions of density, which is mass per volume?

Newton’s law of universal gravitation is represented by F = GMm/r 2 where F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg • m/s2. What are the SI units of the proportionality constant G?

The speed v of an object is given by the equation v = At 3 - Bt, where t refers to time.(a) What are the dimensions of A and B?(b) What are the SI units for the constants A and B?

(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

Kinetic energy K has dimensions kg•m2/s2. It can be written in terms of the momentum p and mass m as K = p2/(2m).(a) Determine the proper units for momentum using dimensional analysis.(b) The unit of force is the newton N where 1 N = 1 kg•m/s2 . What are the units of momentum p in terms of a newton and another fundamental SI unit?

Three students derive the following equations in which x refers to distance traveled, v the speed, a the acceleration (m/s2), t the time, and the subscript zero means a quantity at time t = 0. Which of these equations could possibly be correct according to a dimensional check?(a) x = vt2 + 2at,(b) x = v0t + 1/2at2,(c) x = v0t + 2at2.

Which of the following equations are dimensionally correct? (a) vf = vi + ax (b) y = (2 m) cos (kx) where k = 2 m-1

Which of the following equations are dimensionally consistent and why? (a) x = 1/2at2(b) t = v/x(c) t = (2x/a)1/2

Physical quantities are generally not purely numerical: They have a particular dimension or combination of dimensions associated with them. Thus, your height is not 74, but rather 74 inches, often expressed as 6 feet 2 inches. Although feet and inches are different units they have the samedimension--length.A. Find the dimensions [V] of volume.Express your answer as powers of length ( l), mass ( m), and time ( t).B. Find the dimensions [v] of speed.Express your answer as powers of length ( l), mass ( m), and time ( t).

What are the possible correct units for g in the SI system of units?Mark all the correct statements among those provided below.A. m/s2B. kg•m/s2C. kgD. N/kgE. m/s

The position of a particle moving under uniform acceleration is some function of time and the acceleration. Suppose we write this position as x = kamtn where k is a dimensionless constant. (a) Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. (b) Can this analysis give the value of k?

Which of the following quantities represent mass?Check all that apply.a) 12.0 lbsb) 0.34 gc) 120 kgd) 1600 kNe) 0.34 mf) 411 cmg) 899 MN

Based on these units, select any of the following expressions that could be valid expressions?

What are possible correct units for weight in the SI system of units?Mark all the correct statements among those provided below.A. m/sB. m/s2C. kgD. kg•m/s2E. N/kgF. N

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