Physics, 03.01.2021 14:00 Yasido888

What is the dimensional consistency of s = Vot + 1/2 at2

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Answer from: alexislacour73

The formula is dimensionally consistent

Explanation:

Dimensional Analysis

There are three fundamental magnitudes in Physics:

L = Length

T = Time

M = Mass

All the formulas and equations that use physical magnitudes must be consistent in their units.

For example, the formula:

$\displaystyle s=v_ot+\frac{1}{2}at^2$

Is used to calculate the distance traveled by an object, knowing its initial speed vo, acceleration a, and time t.

The units for each magnitude are:

s = L

vo = L/T or $LT^{-1}$

a = L/T^2 or $LT^{-2}$

Let's analyze the dimensions of the magnitudes in the formula (the constant 1/2 is neglected because it doesn't affect the dimensional analysis):

$\displaystyle L=L/T*T+L/T^2*T^2$

The first term simplifies to L because the T's simplify. The same happens with the second term, the squared T's simplify:

$\displaystyle L=L+L$

Thus the formula is dimensionally consistent

Answer from: Quest

m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| = √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| = √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| = 14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

Answer from: Quest

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