Calculate signed momentum

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Momentum equals mass in kilograms multiplied by signed velocity in meters per second. Formula: a*b. Variable key: a = mass (kg), b = signed velocity (m/s)
• Distinct worked inputs and result: A distinct object has 3 kg mass and -4 m/s velocity: 3×(-4)=-12 kg·m/s.
• Assessment case 1: Supplied case 1: mass (kg)=2; signed velocity (m/s)=3, using the explicitly named quantities. Momentum equals mass in kilograms multiplied by signed velocity in meters per second. What result follows?
• Assessment case 2: Supplied case 2: mass (kg)=3; signed velocity (m/s)=-2, using the explicitly named quantities. Momentum equals mass in kilograms multiplied by signed velocity in meters per second. What result follows?
• Assessment case 3: Supplied case 3: mass (kg)=4; signed velocity (m/s)=5, using the explicitly named quantities. Momentum equals mass in kilograms multiplied by signed velocity in meters per second. What result follows?
• Assessment case 4: Supplied case 4: mass (kg)=5; signed velocity (m/s)=-3, using the explicitly named quantities. Momentum equals mass in kilograms multiplied by signed velocity in meters per second. What result follows?
• Assessment case 5: Supplied case 5: mass (kg)=6; signed velocity (m/s)=2, using the explicitly named quantities. Momentum equals mass in kilograms multiplied by signed velocity in meters per second. What result follows?
• Assessment case 6: Supplied case 6: mass (kg)=2.5; signed velocity (m/s)=-4, using the explicitly named quantities. Momentum equals mass in kilograms multiplied by signed velocity in meters per second. What result follows?

Learn the idea

Momentum is mass times signed velocity. Choosing a positive direction is essential. Opposite velocities give opposite momenta, while mass stays positive.

Momentum equals mass in kilograms multiplied by signed velocity in meters per second. The formula in the supplied model is a*b. Variable key: a = mass (kg), b = signed velocity (m/s). Include velocity direction through its sign. Momentum is not kinetic energy.

A distinct object has 3 kg mass and -4 m/s velocity: 3×(-4)=-12 kg·m/s. Mass does not become negative when motion reverses. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with mass (kg)=3; signed velocity (m/s)=3. Expected result: 9 kg·m/s. Explain what changes and keep this assumption: Mass does not become negative when motion reverses.

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