Acceleration

College/University

Definition

Can be thought of as the increase of something's speed. Acceleration tells you the rate of change in veolicty of an object in relation to time. A positive acceleration means there is an increase in acceleration (speed) and a negative acceleration means there is a decrease in speed.

Worked examples

\(a = \frac{\Delta v}{\Delta t} = \frac{30 \, \)m/s\( - 10 \, \)m/s\(}{4 \, \)s\(} = 5 \, \)m/s\(^2\)

Acceleration is change in velocity divided by time; here speed increased 20 m/s over 4 seconds.

\(a = \frac{0 \, \)m/s\( - 20 \, \)m/s\(}{5 \, \)s\(} = -4 \, \)m/s\(^2\)

Negative acceleration (deceleration) means the object is slowing down.

Common mistakes

\(a = \frac{\)distance\(}{\)time\(}\) → \(a = \frac{\)change in velocity\(}{\)time\(}\) Acceleration is rate of change of velocity, not distance. Distance over time is average speed.
Negative acceleration always means moving backward → Negative acceleration means slowing down (or speeding up in the negative direction) The sign tells you the direction of the acceleration vector, not necessarily backward motion.
\(a = \frac{v}{t}\) → \(a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}\) You must use the change in velocity (final minus initial), not just the final velocity.

Where you'll use it next

You'll apply acceleration in kinematics equations, projectile motion, Newton's second law, and calculus when velocity is given as a function of time and you differentiate to find acceleration.

Found in 1 StudyPug lesson

Position, Velocity, and Acceleration as Derivatives

Calculus 1

Discover how taking derivatives of a position function gives velocity and acceleration, and how their signs describe motion.

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