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Misha Larkins [42]
3 years ago
6

A sled with no initial velocity accelerates at a rate of 3.2 m/s2 down a hill. How long does it take the sled to go 15 m to the

bottom? *
Physics
1 answer:
grin007 [14]3 years ago
3 0
S = ut + 1/2 at^2
a = 3.2 m/s^2
s = 15m
Find t
15 = 1/2(3.2)t^2
15 = 3.2t^2/2
30 = 3.2t^2
30/ 3.2 = 9.38
Square root of 9.38 = 3.06
It takes 3.06 seconds
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Based on the following equation, answer the questions below. ρ = (2γϕ + ψ)/rg where ρ [=] moles per cubic foot [mol/ft3] γ [=] j
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1) Fundamental units of \Psi are [\frac{mol}{m\cdot s^2}]

2) Fundamental units of \Phi are [\frac{mol}{m^3}]

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The equation for the variable \rho is

\rho =\frac{2\gamma \Phi+\Psi}{rg}

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We can re-write the equation as

\rho rg = 2\gamma \Phi + \Psi

And we notice that the units of the term on the left must be equal to the units of the term on the right.

This means that:

1) First of all, \Psi must have the same units of \rho r g. So,

[\rho r g]=[\frac{mol}{ft^3}][in][\frac{m}{s^2}]

However, both ft (feet) and in (inches) are not fundamental dimensions: this means that they can be expressed as meters. Therefore, the fundamental units of \Psi are

[\Psi]=[\frac{mol}{m^3}][m][\frac{m}{s^2}]=[\frac{mol}{m\cdot s^2}]

2)

The term 2\gamma \Phi must have the same units of \Psi in order to be added to it. Therefore,

[\gamma \Phi] = [\frac{mol}{m\cdot s^2}]

We also know that the units of \gamma are [\frac{J}{kg}], therefore

[\frac{J}{kg}][\Phi]= [\frac{mol}{m\cdot s^2}]

And so, the fundamental units of \Phi are

[\Phi]= [\frac{mol\cdot kg}{J\cdot m\cdot s^2}]

However, the Joules can be written as

[J]=[kg][\frac{m^2}{s^2}]

Therefore

[\Phi]= [\frac{mol\cdot kg}{(kg \frac{m^2}{s^2})\cdot m\cdot s^2}]=[\Phi]= [\frac{mol}{m^3}]

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