Constant Acceleration

Overview

Students apply the one-dimensional constant-acceleration equations to solve physics problems involving displacement, velocity, acceleration, and time. Building on prior work with motion graphs, units, and algebra, students will read technical descriptions, translate information into equations and organized tables, and judge whether answers are physically reasonable.

Learning intentions

Students will be able to:

• Define displacement, initial velocity, final velocity, acceleration, and time using correct units.
• Choose and state a coordinate system and sign convention.
• Select and use an appropriate constant-acceleration equation.
• Explain each solution with organized work, units, and textual or visual evidence.

Prerequisite knowledge: Students should be able to distinguish distance from displacement, interpret basic position-time and velocity-time graphs, rearrange algebraic equations, and convert between common units such as seconds and meters per second.

Success criteria

• I can identify known and unknown quantities and include their units.
• I can state a positive direction and assign signs consistently.
• I can choose an equation, substitute values, and solve accurately.
• I can check whether my answer’s units, sign, and magnitude are physically reasonable.

Curriculum links

• Translate quantitative information in technical text into tables, equations, or other visual forms, and translate equations into words.
• Read and comprehend grade-appropriate science and technical texts independently.
• Follow a precise multistep problem-solving procedure, attending to conditions such as constant acceleration.
• Analyze relationships among technical terms and cite specific details from a science or technical description.
• Use precise domain vocabulary and interpret technical terms in context.

Lesson structure (55 minutes)

1. 0–5 min · Launch. Display a short scenario on the opening scenario slide: “A skateboarder starts from rest and accelerates downhill at (2.0\ \text{m/s}^2) for 4.0 s. How fast and how far might the skateboarder travel?” Students estimate independently, then share what information they would need and what direction should be positive.

2. 5–16 min · Explicit instruction. Use the vocabulary and equations slides to define displacement (\Delta x=x_f-x_i) in meters, initial velocity (v_i) and final velocity (v_f) in m/s, acceleration (a) in m/s², and time (t) in seconds. Emphasize that velocity and displacement can be positive or negative, while acceleration describes the rate of change of velocity. Introduce a coordinate system before calculating: for example, “right/uphill is positive.” Model the four equations:

• (v_f=v_i+at)
• (\Delta x=v_it+\frac12at^2)
• (v_f^2=v_i^2+2a\Delta x)
• (\Delta x=\frac{v_i+v_f}{2}t)

Explain that these equations apply when acceleration is constant. Students annotate a five-column table: quantity, symbol, meaning, unit, and sign.

3. 16–25 min · Teacher think-aloud. Solve the launch problem aloud using the think-aloud worked example. State the positive direction, list knowns and unknowns, select the equation, substitute with units, calculate, and check: (v_f=0+(2.0)(4.0)=8.0\ \text{m/s}); (\Delta x=0(4.0)+\frac12(2.0)(4.0)^2=16\ \text{m}). Ask students to identify the textual evidence that indicates “starts from rest” means (v_i=0), and to explain why both results are positive. Students complete each step on their whiteboards and hold them up for checks.

4. 25–39 min · Guided practice and gradual release. Distribute the Constant Acceleration Worksheet. Complete one selected problem together, requiring students to underline given data and box the requested quantity. Pairs then solve two selected problems, one with an object slowing down and one requiring the equation without time. Partners must explain their equation choice using a sentence frame: “I chose ___ because the known quantities include ___ and the unknown is ___.” Circulate, checking signs, units, and algebra. Students then independently attempt a third selected problem while the teacher samples whiteboards and addresses errors immediately.

5. 39–48 min · Technical reading and discussion. Display the translation and reasonableness-check slides with a short paragraph describing a car moving west, slowing uniformly, and stopping. Students convert the paragraph into a known/unknown table and a signed equation set, then translate the equation (v_f=v_i+at) into words. Groups compare answers and cite the precise words that establish direction, initial velocity, and constant acceleration. Discuss why a negative acceleration does not always mean the object is slowing down.

6. 48–55 min · Exit ticket and closure. Students complete the exit ticket below independently on a half-sheet or the final section of the worksheet exit-ticket section. Before collecting, students use the final checklist slide to check direction, equation, work, units, and reasonableness.

Resources

• the Constant Acceleration instructional slide deck
• the Constant Acceleration Worksheet
• Whiteboards and markers
• Calculators
• Student notebooks or paper
• Projector or interactive display
• Half-sheets for exit tickets

Assessment

• Formative checks: vocabulary/table responses, whiteboard equation selection, and teacher observation of pair work.
• Require students to explain equation choice and cite words from the technical scenario, not only report a numerical answer.
• Exit ticket success: 4 points—appropriate coordinate system, correct equation and substitution, accurate answer with units, and a reasonable-answer check.

Exit ticket: A cyclist traveling east at (6.0\ \text{m/s}) accelerates uniformly at (-1.5\ \text{m/s}^2) for (3.0\ \text{s}). a. Find the final velocity. b. Find the displacement during the 3.0 s. c. State whether the cyclist is still moving east or has reversed direction, and justify your answer.

Answer key: Let east be positive. Known: (v_i=+6.0\ \text{m/s}), (a=-1.5\ \text{m/s}^2), (t=3.0\ \text{s}). a. (v_f=v_i+at=6.0+(-1.5)(3.0)=+1.5\ \text{m/s}). b. (\Delta x=v_it+\frac12at^2=(6.0)(3.0)+\frac12(-1.5)(3.0)^2=18.0-6.75=+11.25\ \text{m}), or (11.3\ \text{m}) to appropriate precision. c. The cyclist is still moving east because (v_f) is positive. The positive displacement also supports this conclusion. Answers must include units and recognize that the negative acceleration reduces eastward velocity.

Differentiation

• Support: provide a formula strip, a labeled known/unknown table, unit reminders, and sentence frames; allow calculator use and partner reading of the technical scenario.
• For EAL students and students needing language support, preteach “uniformly,” “opposite,” “from rest,” and “comes to a stop,” with arrows and a completed example.
• For students needing additional support, assign worksheet problems in increasing complexity and conference after the first pair problem.
• Extension: students compare two valid equations for the same problem, explain why both work, or create a motion scenario whose acceleration is negative while velocity remains positive.

Common misconceptions and corrective teaching moves

• “Negative acceleration always means slowing down.” Have students compare velocity and acceleration signs: same signs increase speed; opposite signs decrease speed.
• “Distance and displacement are interchangeable.” Draw the coordinate line and ask students to report both path length and signed change in position.
• “The final velocity is always zero.” Return to the wording: only “stops,” “comes to rest,” or an equivalent statement sets (v_f=0).
• “Any equation can be used with any data.” Require students to circle known quantities and cross out equations containing an additional unknown.
• “A negative answer is automatically wrong.” Ask whether the sign matches the chosen direction, then check units and magnitude.