Question

1. Convert:- a. 4000 cm2to m2
b. 54 km/h to m/s
c. 5.2 g/cm3to kg/m3

2. A car travels a distance of 60 km in 1.5 hours
a. What is its speed? b. Express its speed in m/s.

Answer 1

Answer:

1.

a. 0.4m²

b. 15m/s

c. 5200kg/m³

2.

a. 40km/h

b. 11.11m/s

Explanation:

01. a. 4000cm²=4000×10⁻⁴m²=4×10³×10⁻⁴m²=4×10³⁺⁽⁻⁴⁾m²=4×10⁻¹m²=0.4m²

Here we know that 1cm=10⁻²m. In the given question, it is cm². So we need to multiply the value by (10⁻²)² i.e., 10⁻⁴.          

b. 54km/h=54×$\frac{1000}{3600}$m/s=54×$\frac{5}{18}$m/s=3×5m/s=15m/s

As we know 1km=1000m and 1h=3600s. So we multiply by 1000 to convert the km into m and divide by 3600 to convert the hour in seconds i.e., $\frac{1000}{3600}$

c. 5.2g/cm³=5.2×(10⁻³/10⁻⁶)kg/m³=5.2×10⁻³⁻⁽⁻⁶⁾kg/m³=5.2×10³kg/m³=5200kg/m³

We know that 1g=10⁻³kg and 1cm=10⁻²m. Thus we multiply 10⁻³ and divide by 10⁻⁶(as it is cm³) to convert the g/cm³ into kg/m³.

02.

a. Given Distance=60km and time=1.5h

We know that,

$speed=\frac{distance}{time}$

Substituting the values

speed=$\frac{60}{1.5}$km/h=40km/h

b. To convert km/h into m/s just multiply by $\frac{5}{18}$

40km/h=40×$\frac{5}{18}$m/s=11.11ms