Motion

Learn position and velocity, velocity and acceleration.

Lesson 1 of 32 parts Practice Flashcards

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Position and Velocity

Objective: Explain position and velocity, apply the stated method, and check its conditions.

Velocity is the derivative of position with respect to time. It is signed, indicating direction along a chosen coordinate axis. Position offsets disappear under differentiation; elapsed-time units determine the denominator of the velocity unit. Negative velocity describes direction, not a negative speed magnitude.

Formulas

$v=s′$

Worked examples

Try itPosition is s(t)=6t³+7. Find velocity at t=7.Show answer

Step 1: Velocity is s′(t)=18t². Step 2: Use t=7. Step 3: Velocity is 882 position units/time unit.

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Position and Velocity

Objective: Explain position and velocity, apply the stated method, and check its conditions.

Formulas

$v=s′$

Worked examples

Try itPosition is s(t)=6t³+7. Find velocity at t=7.Show answer

Step 1: Velocity is s′(t)=18t². Step 2: Use t=7. Step 3: Velocity is 882 position units/time unit.

Velocity and Acceleration

Objective: Explain velocity and acceleration, apply the stated method, and check its conditions.

Acceleration is the derivative of velocity and the second derivative of position. Its sign alone does not determine speeding up: speed increases when velocity and acceleration have the same sign and decreases when their signs differ, away from zero-velocity transitions. Positive acceleration does not always mean increasing speed.

Formulas

$a=v′=s″$

Worked examples

Try itPosition is s(t)=6t³+7t. Find acceleration at t=7.Show answer

Step 1: Acceleration is the second derivative of position. Step 2: s′(t)=18t²+7; s″(t)=36t. Step 3: Acceleration at 7 is 252.

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