Given data

• Mass: $m = 3.513\,\text{kg}$
• Speed: $v = 5.00\,\text{m s}^{-1}$

Formula for momentum

The magnitude of momentum is $p = mv$

Substitute the values

$p = 3.513 \times 5.00$

$p = 17.565\,\text{kg m s}^{-1}$

Apply significant figures

• $3.513$ has 4 significant figures
• $5.00$ has 3 significant figures

In multiplication, the result should have the same number of significant figures as the factor with the least number of significant figures.

So, the answer should be reported to 3 significant figures.

$17.565 \to 17.6$

Match with options

• A: $17.6\,\text{kg m s}^{-1}$ ✅
• B: $17.565\,\text{kg m s}^{-1}$ ❌ (too many significant figures)
• C: $17.56\,\text{kg m s}^{-1}$ ❌
• D: $17.57\,\text{kg m s}^{-1}$ ❌

Final answer

The correct recorded magnitude of momentum is $\boxed{17.6\,\text{kg m s}^{-1}}$