Constant-Acceleration Calculations

Learn the models, terms, and applications of constant-acceleration calculations.

Lesson 3 of 32 parts Practice Flashcards

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Free Fall as a Model

Objective: Describe gravitational acceleration and its assumptions.

Near Earth’s surface, freely falling objects have approximately constant downward acceleration of magnitude 9.8 m/s² if air resistance is negligible. This is an idealized model, and actual motion depends on drag and conditions. If upward is positive, acceleration is about −9.8 m/s² both while an object travels upward and while it travels downward; at the highest point, instantaneous vertical velocity is zero but acceleration is not. Objects of different masses have the same ideal free-fall acceleration in the same gravitational field when drag is neglected. Motion calculations should state the coordinate direction and approximation used.

Worked examples

Try itAt the top of an ideal upward toss, what is vertical acceleration?Show answer

1. Identify the relevant concept in this section. 2. Gravity still acts at the peak. 3. Answer: Approximately 9.8 m/s² downward

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Free Fall as a Model

Objective: Describe gravitational acceleration and its assumptions.

Worked examples

Try itAt the top of an ideal upward toss, what is vertical acceleration?Show answer

1. Identify the relevant concept in this section. 2. Gravity still acts at the peak. 3. Answer: Approximately 9.8 m/s² downward

Applications and Worked Problems

Objective: Apply constant-acceleration calculations to calculations, evidence, and specified situations.

For one-dimensional constant acceleration, use v=u+at, Δx=ut+½at², and v²=u²+2aΔx. These equations require constant acceleration over the analyzed interval. Choose signs for velocity, displacement, and acceleration consistently. Free-fall examples neglect air resistance and use g=9.8 m/s² near Earth; upward-positive and downward-positive choices are both valid if used consistently. At a turning point velocity can be zero while acceleration remains nonzero.

Formulas

$v=u+at$
$Δx=ut+½at²$
$v²=u²+2aΔx$

Worked examples

Try itAn object starts at 1 m/s and accelerates at 1 m/s² for 3 s. Find final velocity.Show answer

1. v=u+at. 2. 1+1×3=4 m/s.

Try itFor u=1 m/s, a=1 m/s², and t=3 s, find displacement.Show answer

1. Δx=ut+½at². 2. 1×3+0.5×1×3²=7.5 m.

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