Calculate kinetic energy

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: Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. Formula: 0.5*a*b*b. Variable key: a = mass (kg), b = speed (m/s)
• Distinct worked inputs and result: A distinct model has mass 2 kg and speed 5 m/s: 0.5×2×25=25 J.
• Assessment case 1: Supplied case 1: mass (kg)=2; speed (m/s)=3, using the explicitly named quantities. Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. What result follows?
• Assessment case 2: Supplied case 2: mass (kg)=4; speed (m/s)=2, using the explicitly named quantities. Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. What result follows?
• Assessment case 3: Supplied case 3: mass (kg)=3; speed (m/s)=4, using the explicitly named quantities. Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. What result follows?
• Assessment case 4: Supplied case 4: mass (kg)=5; speed (m/s)=6, using the explicitly named quantities. Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. What result follows?
• Assessment case 5: Supplied case 5: mass (kg)=6; speed (m/s)=5, using the explicitly named quantities. Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. What result follows?
• Assessment case 6: Supplied case 6: mass (kg)=8; speed (m/s)=3, using the explicitly named quantities. Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. What result follows?

Learn the idea

Translational kinetic energy is one-half mass times speed squared in this classical model. It is nonnegative and depends on speed magnitude; opposite velocities with equal speed have equal kinetic energies.

Kinetic energy equals one-half mass in kilograms multiplied by speed in meters per second squared. The formula in the supplied model is 0.5*a*b*b. Variable key: a = mass (kg), b = speed (m/s). Square speed before multiplying. Kinetic energy does not have a directional sign.

A distinct model has mass 2 kg and speed 5 m/s: 0.5×2×25=25 J. This formula concerns translational motion. 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; speed (m/s)=3. Expected result: 13.5 J. Explain what changes and keep this assumption: This formula concerns translational motion.

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