Calculate constant acceleration

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: Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. Formula: (a-b)/c. Variable key: a = final velocity (m/s), b = initial velocity (m/s), c = elapsed time (s)
• Distinct worked inputs and result: A distinct model changes from 2 to 8 m/s in 3 s: (8-2)/3=2 m/s².
• Assessment case 1: Supplied case 1: final velocity (m/s)=12; initial velocity (m/s)=4; elapsed time (s)=2, using the explicitly named quantities. Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. What result follows?
• Assessment case 2: Supplied case 2: final velocity (m/s)=15; initial velocity (m/s)=3; elapsed time (s)=4, using the explicitly named quantities. Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. What result follows?
• Assessment case 3: Supplied case 3: final velocity (m/s)=6; initial velocity (m/s)=10; elapsed time (s)=2, using the explicitly named quantities. Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. What result follows?
• Assessment case 4: Supplied case 4: final velocity (m/s)=20; initial velocity (m/s)=5; elapsed time (s)=3, using the explicitly named quantities. Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. What result follows?
• Assessment case 5: Supplied case 5: final velocity (m/s)=-2; initial velocity (m/s)=4; elapsed time (s)=3, using the explicitly named quantities. Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. What result follows?
• Assessment case 6: Supplied case 6: final velocity (m/s)=18; initial velocity (m/s)=6; elapsed time (s)=4, using the explicitly named quantities. Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. What result follows?

Learn the idea

Acceleration is change in velocity per time, including direction through signs. Average acceleration does not imply every instant is constant. The supplied straight-line models state constant acceleration.

Acceleration equals final velocity minus initial velocity, divided by elapsed seconds. The formula in the supplied model is (a-b)/c. Variable key: a = final velocity (m/s), b = initial velocity (m/s), c = elapsed time (s). Keep final minus initial order. Acceleration can be negative while speed increases in a negative direction.

A distinct model changes from 2 to 8 m/s in 3 s: (8-2)/3=2 m/s². Use the stated coordinate direction. 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 final velocity (m/s)=13; initial velocity (m/s)=4; elapsed time (s)=2. Expected result: 4.5 m/s². Explain what changes and keep this assumption: Use the stated coordinate direction.

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