Question

Write the conversion factor(s) for (a) cm/min to in/s (b) m3 to in3 (C) m/s2 to km/h2

Answer 1

Answer :

(a) $1cm/min=6.56\times 10^{-3}in/s$

(b) $1m^3=61023.7in^3$

(c) $1m/s^2=7.716\times 10^{-11}km/hr^2$

Explanation:

(a) cm/min to in/s

The conversion factor used :

$1cm=\frac{1}{2.54}in$

and,

$1min=60s$

So, $\frac{1cm}{1min}\times \frac{1in}{2.54cm}\times \frac{1min}{60s}$

$\Rightarrow 6.56\times 10^{-3}in/s$

Thus, $1cm/min=6.56\times 10^{-3}in/s$

(b) $m^3\text{ to }in^3$

The conversion factor used :

$1m^3=61023.7in^3$

Thus, $1m^3=61023.7in^3$

(c) $m/s^2\text{ to }km/hr^2$

The conversion factor used :

$1m=\frac{1}{1000}km$

and,

$1s=\frac{1}{3600}hr$

So, $\frac{1m}{1s^2}\times \frac{1km}{1000m}\times \frac{1s^2}{3600\times 3600hr^2}$

$\Rightarrow 7.716\times 10^{-11}km/hr^2$

Thus, $1m/s^2=7.716\times 10^{-11}km/hr^2$

Answer 2

Answer:The conversion factors are :

a) 1cm/min = 0.00657in/s

b) 1m3= 61023.378in3

c) 1m/s2=12960km/hr

Explanation:

In Physics, there are fundamental units and these are the units for fundamental quanties, Time (seconds), temperature (K), current (Ampere), amount of substance (Mol) ,Luminous intensity (candela), length (metre), mass (Kilogram).

Apart these fundamental units, other units are known as derived units , because they were derived from combination of at least two of these fundamental quantity. Examples are Velocity ( metre/seconds) and volume (m3)

The various units are groupas SI( International system of unit) and non - SI units.

The SI units of Time is seconds while other non-SI units are hour , minutes,days and year. These non SI units are also acceptable and can be converted to either SI unit or another non -SI unit using a specified conversion factor.

For the given units.

a) cm/min to in/s

Both are unit for velocity and they are non-SI unit, because the standard unit of velocity is m/s.

Therefore , it involves converting from one non-SI unit to another non-SI unit.

1cm/min means 1cm/1min

And 1 in/s = 1 in/1min

1cm = 0.394in

1min= 60s

Therefore 1/cm/min= 0.394in/60s

==> 1cm/min= 0.00657in/s

b) m² to in²

Both are unit for volume and m² is the SI unit and in3 is a non-SI unit .

Therefore , it involves converting from SI unit to another non-SI unit.

1m3 = 1m × 1m ×1m

1in3= 1in × 1in× 1in

Where 1m =39.370in

Therefore 1m3= 39.370 × 39.370 ×39.370

1m3 = 61023.378in3

c) m/s² to km/h²

Both are unit for acceleration and m/s² is the SI unit and km/h²is a non SI unit .

Therefore , it involves converting from SI unit to another non-SI unit.

1m/s² =1km/1h²

1m= 0.001km

1s² =1s × 1s

1h²= 1h × 1h

1s = (1/3600)hr

1s²= (1/3600) ×(1/3600) h = 1/12960000hr

1m/s2 = 0.001km/ (1/12960000hr)

1m/s2 = 12960km/hr

There the conversion factors are :

a) 1cm/min= 0.00657in/s

b) 1m3 = 61023.378in3

c) 1m/s2 = 12960km/hr