Consider the physical quantities s, a, and t with dimensions [s] = L, [v] = LT-!, [a] = LT -2, v, and [t] = T. Determine whether each of the following equations is dimensionally consistent: (a) s = vt + 0.5at2; (b) s = vt² + 0.5at; and (c) v = sin(ar²/s). a) Only "a" is consistent b) Only "b" is consistent c) Only "c" is consistent d) All equations are consistent

Instrument Ruler Quantities Diameter Units m Meas #1 Meas #2 Meas #3 Meas #4 Meas #5 Meas #6 0.011 0.017 0.019 0.016 0.009 0.021 Vernier Caliper Micro-meter Diameter Diameter 0.0120 0.0166 0.0182 0.0151 0.0100 0.0225 0.01268 0.01745 0.01904 0.01587 0.00947 0.02221 Ruler Volume 7.0E-07 2.6E-06 3.6E-06 2.1E-06 4.E-07 4.8E-06 Measurements: diameter and volume. Results: mass Vernier Caliper Volume Measurements: diameter and mass. Results: volume O Measurements: diameter and mass. Results: none. 9.05E-07 2.40E-06 3.16E-06 1.80E-06 5.24E-07 5.96E-06 Among this data, what is considered raw measurement and plain result? Micro-meter Volume 1.067E-06 2.782E-06 3.614E-06 2.093E-06 4.45E-07 5.736E-06 Measurements: diameter measured with the ruler only and mass. Results: volume. Scale Mass kg 0.00850 0.02080 0.02720 0.01680 0.00389 0.04423

..................... The dimensions of the quantity kinetic energy, designated by K, are kg m/s, It can be written in terms of the momentum p and mass m as K = 2m (a) What are the units of momentum in terms of fundamental SI units? (Use the following as necessary: kg, m, and s.) [P) - (b) Force is measure in units of newtons, N, where 1N- 1 kg m/s. What are the units of momentum p in terms of a newton and another fundamental SI unit? (Use the. following as necessary: N, m, and s.) [P) = (c) What If? Physicists often measure the momentum of subatomic particles moving near the speed of light in units of MeV/c, where c is the speed of light, and 1 Mev = 1.6 x 101 kg m/s. Based on this, what are the units of momentum for a high-speed subatomic particle in terms of fundamental SI units? What are the units of momentum for a high-speed subatomic particle in terms of a newton and another fundamental SI unit? [P] -

Consider the physical quantities m, s, v, a, t, and r with dimensions [m] = M, [s] = L, [v] = LT–1, [a] = LT–2, [t] = T, and [r] = L. Assuming each of the following equations is dimensionally consistent, find the dimension of the quantity on the left-hand side of the equation: (a) F = ma; (b) K = 0.5mv2; (c) p = mv; (d) W = mas; (e) L = mvr.

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

P is pressure, x distance and v velocity. What are the units of k so that the equation v = K dP/dx is dimensionally correct? (A) m/s (B) m^3s / kg (C) kg / (m s^3) D) k has no units

I need help with a University Physics 1 (significant figures) - The problem is described in the image below:

An engineer uses a stopwatch to measure the duration of an event. The digital stopwatch reading shows 0.77 s. (a) What uncertainty is implied by the reading itself without any other knowledge? (b) Suppose the stopwatch manufacturer specifications state an error of up to 1% of the reading. What value of uncertainty might you state with the reading? (c) Suppose the engineer adds an uncertainty of 0.05 s due to reaction time. What uncertainty might you state with the reading?