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What is the momentum of a [tex]$1.5 \times 10^3$[/tex] kilogram van that is moving at a velocity of 32 meters/second?

A. 46.9 kilogram meters/second
B. [tex]$4.7 \times 10^3$[/tex] kilogram meters/second
C. [tex][tex]$4.85 \times 10^2$[/tex][/tex] kilogram meters/second
D. [tex]$4.85 \times 10^4$[/tex] kilogram meters/second


Sagot :

To determine the momentum of a van with a mass of [tex]\(1.5 \times 10^3\)[/tex] kilograms and a velocity of 32 meters per second, we use the formula for momentum:

[tex]\[ \text{Momentum} = \text{Mass} \times \text{Velocity} \][/tex]

Substitute the given values:

[tex]\[ \text{Momentum} = 1.5 \times 10^3 \, \text{kg} \times 32 \, \text{m/s} \][/tex]

Perform the multiplication:

[tex]\[ \text{Momentum} = (1.5 \times 32) \times 10^3 \][/tex]

Calculating [tex]\(1.5 \times 32\)[/tex] gives:

[tex]\[ 1.5 \times 32 = 48 \][/tex]

So,

[tex]\[ \text{Momentum} = 48 \times 10^3 \, \text{kg} \cdot \text{m/s} \][/tex]

This can be written as:

[tex]\[ \text{Momentum} = 4.8 \times 10^4 \, \text{kg} \cdot \text{m/s} \][/tex]

The correct answer is:

D. [tex]\(4.85 \times 10^4\)[/tex] kilogram meters/second

However, the exact calculation without any rounding should be:

[tex]\[ \text{Momentum} = 48000 \, \text{kg} \cdot \text{m/s} \][/tex]

And matching this with the closest value, the final correct answer is:

D. [tex]\( 4.85 \times 10^4 \)[/tex] kilogram meters/second