Changing Velocity

Learn the models, terms, and applications of changing velocity.

Lesson 1 of 32 parts Practice Flashcards

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Average Acceleration

Objective: Compute change in velocity divided by time.

Average acceleration in one dimension is a_avg = (v_f − v_i)/Δt, with SI unit m/s². A velocity change from 2 m/s to 10 m/s over 4 s corresponds to +2 m/s². Acceleration describes a change in velocity, which can reflect a change in speed, direction, or both. A negative acceleration is acceleration in the negative coordinate direction and is not automatically slowing down: an object moving left and accelerating left can gain speed. Acceleration calculations require velocities in the same reference frame and a positive, stated time interval.

Worked examples

Try itVelocity changes from +2 m/s to +10 m/s in 4 s. What is average acceleration?Show answer

1. Identify the relevant concept in this section. 2. Change of +8 m/s over 4 s is +2 m/s². 3. Answer: +2 m/s²

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Average Acceleration

Objective: Compute change in velocity divided by time.

Worked examples

Try itVelocity changes from +2 m/s to +10 m/s in 4 s. What is average acceleration?Show answer

1. Identify the relevant concept in this section. 2. Change of +8 m/s over 4 s is +2 m/s². 3. Answer: +2 m/s²

Applications and Worked Problems

Objective: Apply changing velocity to calculations, evidence, and specified situations.

Average acceleration is the signed velocity change divided by elapsed time. A positive acceleration does not always mean increasing speed: compare its direction with velocity. If they have the same sign in one dimension, speed increases; if opposite signs, speed initially decreases. The definition applies to the interval average, while instantaneous acceleration describes a limit over a very short interval. State an inertial reference frame and axis before using signs.

Formulas

$a_avg=(v_f−v_i)/Δt$
Δv=aΔt for constant a

Worked examples

Try itWith east positive, velocity changes from +1 to +6 m/s in 3 s. Find average acceleration.Show answer

1. a=(v_f−v_i)/Δt. 2. (6−1)/3=1.667 m/s².

Try itA westward velocity changes from −1 to −6 m/s over 3 s. Find signed acceleration.Show answer

1. Use signed velocities. 2. (−6−(−1))/3=-1.667 m/s².

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