The change in velocity divided by the elapsed time: $a_{avg}=\Delta v/\Delta t$.

Acceleration as a vector

Acceleration is a vector because it describes the change in vector velocity.

Negative acceleration

It points along the negative direction of the chosen coordinate axis; it does not alone indicate slowing down.

Velocity and acceleration in straight-line motion

The same direction means speed increases; opposite directions mean speed decreases.

Classical mechanicsLesson 2 of 2 in the course Motion Along a Straight Line

Average and Instantaneous Acceleration: Definitions, Graphs, and Direction

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Summary

Acceleration describes how velocity changes over time. It helps explain familiar events such as a car speeding up or braking, and also the motion of particles in accelerators and space.

$a_{avg} = \frac{\Delta v}{\Delta t} = \frac{v_f-v_0}{t_f-t_0}$

Here, $v_0$ and $v_f$ are the initial and final velocities, and $t_0$ and $t_f$ are the corresponding times. Velocity is measured in meters per second, and time in seconds, so acceleration is measured in meters per second squared ( $\text{m/s}^2$ ).

All flashcards

Average acceleration: The change in velocity divided by the elapsed time: $a_{avg}=\Delta v/\Delta t$ .
Instantaneous acceleration: The derivative of velocity with respect to time: $a(t)=dv/dt$ .
Acceleration as a vector: Acceleration is a vector because it describes the change in vector velocity.
Negative acceleration: It points along the negative direction of the chosen coordinate axis; it does not alone indicate slowing down.
Velocity and acceleration in straight-line motion: The same direction means speed increases; opposite directions mean speed decreases.

Quiz questions

A horse changes velocity from $0$ to $-15.0\,\text{m/s}$ in $1.80\,\text{s}$ , with east defined as positive. What is its average acceleration?Answer: $-8.33\,\text{m/s}^2$ , directed west.
A runner reverses direction while maintaining the same speed. What happens to the runner's velocity?Answer: It changes because velocity includes direction.
An object moves east while accelerating west along a straight line. What happens to its speed at that moment?Answer: It decreases because acceleration is opposite to velocity.
When acceleration varies during motion, how do average and instantaneous acceleration differ?Answer: Average acceleration describes an interval; instantaneous acceleration describes one moment.
A velocity-versus-time graph is a straight line. What does this indicate about acceleration?Answer: Acceleration is constant because the graph's slope is constant.

Based on University Physics Volume 1 by William Moebs, Samuel J. Ling, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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