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 acceleration: Derivative

Calculus 1

We now know that taking the derivative of a function will give us the slope, or the instantaneous rate of change of the function. So what if we take the derivative of a function that models the position of some object moving along a line? It gives us its velocity! And if we differentiate its velocity function? It gives us its acceleration! In this section, we will study the relationship between position, velocity and acceleration using our knowledge of differential calculus.

UniversityUniversity