Questions: Problem: Momentum is mass times velocity. Suppose the momentum of a 495 g object is measured to be 286. kg*m/s. Calculate the object's velocity. Be sure your answer has a unit symbol and the correct number of significant digits.

Problem: Momentum is mass times velocity. Suppose the momentum of a 495 g object is measured to be 286. kg*m/s. Calculate the object's velocity. Be sure your answer has a unit symbol and the correct number of significant digits.
Transcript text: Problem: Momentum is mass times velocity. Suppose the momentum of a $495 . \mathrm{g}$ object is measured to be 286. $\frac{\mathrm{kg} \cdot \mathrm{m}}{\mathrm{s}}$. Calculate the object's velocity. Be sure your answer has a unit symbol and the correct number of significant digits.
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Solution

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Solution Steps

Step 1: Convert Mass to Kilograms

First, we need to convert the mass from grams to kilograms. The mass of the object is given as \(495 \, \text{g}\).

\[ 495 \, \text{g} = 0.495 \, \text{kg} \]

Step 2: Use the Momentum Formula

The formula for momentum (\(p\)) is given by:

\[ p = m \cdot v \]

where \(m\) is the mass and \(v\) is the velocity. We need to solve for \(v\).

Step 3: Solve for Velocity

Rearrange the formula to solve for \(v\):

\[ v = \frac{p}{m} \]

Substitute the given values into the equation:

\[ v = \frac{286 \, \frac{\text{kg} \cdot \text{m}}{\text{s}}}{0.495 \, \text{kg}} \]

Step 4: Calculate the Velocity

Perform the division to find the velocity:

\[ v = \frac{286}{0.495} \approx 577.7778 \, \text{m/s} \]

Step 5: Round to Correct Significant Digits

The given values have three significant digits, so we should round the velocity to three significant digits as well:

\[ v \approx 578 \, \text{m/s} \]

Final Answer

\[ \boxed{v = 578 \, \text{m/s}} \]

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