<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
Our Terms of Use (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use.

Velocity and Acceleration

The speed and direction of a moving object and how that rate changes over time.

Atoms Practice
Estimated8 minsto complete
Practice Velocity and Acceleration
Estimated8 minsto complete
Practice Now
Turn In
Velocity and Acceleration

Students will learn the meaning of acceleration, how it is different than velocity and how to calculate average acceleration.

Key Equations

\begin{align*}v =\end{align*}v= velocity (m/s)

\begin{align*}v_i =\end{align*}vi= initial velocity

\begin{align*}v_f =\end{align*}vf= final velocity

\begin{align*}\Delta v =\end{align*}Δv= change in velocity \begin{align*}= v_f - v_i\end{align*}=vfvi

\begin{align*}v_{avg} = \frac{\Delta x}{\Delta t}\end{align*}vavg=ΔxΔt

\begin{align*}a =\end{align*}a= acceleration \begin{align*}(m/s^2)\end{align*}(m/s2)

\begin{align*}a_{avg} = \frac{\Delta v}{\Delta t}\end{align*}aavg=ΔvΔt

  • Acceleration is the rate of change of velocity. So in other words, acceleration tells you how quickly the velocity is increasing or decreasing. An acceleration of \begin{align*} 5 \ m/s^2 \end{align*}5 m/s2 indicates that the velocity is increasing by \begin{align*} 5 m/s \end{align*}5m/s in the positive direction every second.
  • Deceleration is the term used when an object’s speed (i.e. magnitude of its velocity) is decreasing due to acceleration in the opposite direction of its velocity.

Example 1

A Top Fuel dragster can accelerate from 0 to 100 mph (160 km/hr) in 0.8 seconds. What is the average acceleration in \begin{align*}m/s^2\end{align*}m/s2?

Question: \begin{align*}a_{avg} = ? \ [m/s^2]\end{align*}aavg=? [m/s2]

Given: \begin{align*}v_i = 0 \ m/s\end{align*}vi=0 m/s

\begin{align*}{\;} \qquad \ \ v_f = 160 \ km/hr\end{align*}  vf=160 km/hr

\begin{align*}{\;} \qquad \ \quad t = 0.8 \ s\end{align*} t=0.8 s

Equation: \begin{align*}a_{avg} = \frac{\Delta v }{t}\end{align*}aavg=Δvt

Plug n’ Chug: Step 1: Convert km/hr to m/s

\begin{align*}v_f = \left( 160 \frac{km}{hr} \right ) \left( \frac{1,000 \ m}{1 \ km} \right ) \left ( \frac{1 \ hr}{3,600 \ s} \right ) = 44.4 \ m/s\end{align*}vf=(160kmhr)(1,000 m1 km)(1 hr3,600 s)=44.4 m/s

Step 2: Solve for average acceleration:

\begin{align*}a_{avg} = \frac{\Delta v}{t} = \frac{v_f - v_i}{t} = \frac{44.4 \ m/s - 0 \ m/s}{0.8 \ s} = 56 \ m/s^2\end{align*}aavg=Δvt=vfvit=44.4 m/s0 m/s0.8 s=56 m/s2

Answer: \begin{align*}\boxed {\mathbf{56 \ m/s^2}}\end{align*}

Watch this Explanation


The Moving Man (PhET Simulation)

Time for Practice

  1. Ms. Reitman’s scooter starts from rest and accelerates at \begin{align*}2.0 m/s^2\end{align*}. What is the scooter's velocity after 1s? after 2s? after 7s?


1. 2 m/s, 4 m/s, 14 m/s

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Velocity and Acceleration.
Please wait...
Please wait...