1. The maximum running speed (S) in km/hr and the corresponding body mass (m) in kg were determined for 55 different species of mammals. An empirical relation was determined to be:
S[km/hr] = 5.7 (m[kg]). Note: The notation in this equation means, "inserting the mass (m) in units of
‘kg', automatically calculates the maximum running speed (S) in units of ‘km/hr.
(a) What are the implied units for the "5.7" factor? Hint: recall that relations between physical quantities
must be dimensionally consistent, and the chosen units must in turn be consistent with the
dimensionality.
(b) Re-write the equation so that it gives the maximum speed in units of “m/s" for a given body mass in
"g”. Show all relevant details. If done correctly, you will need to use at least one unit conversion
factor.

A) 5.7 = (S/m)(km/(kg•hr))  

B) S (m/s) = 5.7(3600m) g

This is about conversion of units.

We are told that the empirical relation is given by;

S[km/hr] = 5.7 (m[kg])

(a) S[km/hr] = 5.7 (m[kg])

Since we are told that;

S is maximum running speed in km/hr

m is mass in kg

Making 5.7 the subject of the formula, we have to divide both sides by (m[kg]) to get;

5.7 = S[km/hr]/(m[kg])

Rearranging gives;

5.7 = (S/m)(km/(kg•hr))

(b) S[km/hr] = 5.7 (m[kg])

We want convert km/hr to m/s.

From conversions, we know that;

36 km/hr = 10 m/s

Thus; S km/hr = 10S/36 m/s = S/3.6 m/s

Similarly, from conversion tables, from kg to g;

1 kg = 1000 g

Thus;

m kg = (1000m) g

Thus; S[km/hr] = 5.7 (m[kg]) can now be expressed as;

S/3.6 m/s = 5.7(1000m) g

Thus, rearranging we have;

S (m/s) = (5.7 × 3.6 × 1000m) g

S (m/s) = 5.7(3600m) g

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(a) [km/hr/kg]

(b) S[m/s] = (5.7 / 3600) (m[g])

Explanation:

(a) S[km/hr] = 5.7 (m[kg])

Solving for 5.7:

5.7 = S[km/hr] / (m[kg])

5.7 = S/m [km/hr/kg]

(b) S[km/hr] = 5.7 (m[kg])

Convert km/hr to m/s.

S[m/s] = S[km/hr] × [1000 m/km] × [1 hr / 3600 s]

S[m/s] = S[km/hr] / 3.6

3.6 S[m/s] = S[km/hr]

Convert kg to g.

m[g] = m[kg] × [1000 g/kg]

m[g] = 1000 m[kg]

m[g] / 1000 = m[kg]

Substitute.

3.6 S[m/s] = 5.7 (m[g] / 1000)

S[m/s] = (5.7 / 3600) (m[g])

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