# Question 23caa

Sep 21, 2015

1. 0.015 km/s
2. 0.0008 J/kg^-1
3. 5 m/s
4. -
5. 8 g/cm^3
6. 50 m/s^-2
7. 4200 J/kg

#### Explanation:

15 m/s to km/s
Note: 1 m = 0.001 km
$15 \frac{m}{s}$
$= 15 \frac{0.001 k m}{s}$
$= \frac{0.015 k m}{s}$

0.8 J/g^-1 to J/kg^-1
Note: 1 g = 0.001 kg
$0.8 \frac{J}{g} ^ - 1$
$= 0.8 \cdot J \cdot g$
$= 0.8 \cdot J \cdot \left(0.001 k g\right)$
$= 0.0008 \cdot J \cdot k g$
$= 0.0008 \frac{J}{k {g}^{-} 1}$

18 km/h to m/s
Note: 1 km = 1000 m; 1 h = 3600 s
$18 \frac{k m}{h}$
$= 18 \frac{1000 m}{3600 s}$
$= 5 \frac{m}{s}$

2.5cm^3 to kg/m
Can I get some clarification on the units of this one? I don't think it's convertible.

8000 kg/m^3 to g/cm^3
Note: 1 kg = 1000 g; 1 m = 100 cm
$8000 \frac{k g}{m} ^ 3$
$= 8000 \frac{1000 g}{100 c m} ^ 3$
=8000(1000g)/((100)^3cm^3#
$= 8 \frac{g}{c {m}^{3}}$

5000 cm/s^-2 to m/s^-2
Note: 1 cm = 0.01 m
$5000 \frac{c m}{s} ^ - 2$
$= 5000 \frac{0.01 m}{s} ^ - 2$
$= 50 \frac{m}{s} ^ - 2$
$4.2 \frac{J}{g}$
$= 4.2 \frac{J}{0.001 k g}$
$= 4200 \frac{J}{k g}$