(FOM) Speed vs. Velocity Lesson

Speed vs. Velocity

Speed is not a new term to you. You commonly refer to how fast you were going in the terms of miles per hour. You might have heard speed and velocity used interchangeably, but they do differ from one another. Speed refers to how fast an object is moving in terms of distance moved and time taken to move in. Velocity is a measure of speed in a given direction. Velocity is important in that it distinguishes the direction the object is traveling. In physics, we use velocity because when comparing different objects' motions it is important to know not only the magnitude but also the direction of the motion.

Calculating Velocity

It is important that we can answer specific questions related to velocity. For instance, "How long does a foot race take?" and "What is the runner's speed?" can only be answered by making calculations. Velocity is calculated by using the following equation:

$LaTeX: v=\frac{\Delta d}{\Delta t}$ $v=\frac{\Delta d}{\Delta t}$

Velocity equals the change in displacement of distance divided by the change in time. Whenever any calculations are performed it is important to include the units. Without units, the numbers are meaningless. The SI unit for velocity is meters per second or m/s, but many other units, such as km/h, mi/h (also written as mph), and cm/s, are in common use.

There are a couple of things to be aware of when calculating velocity problems.

The problem could ask for you to find velocity, distance, or time. You will need to be able to rearrange the problem in order to find the missing variable. You can use algebra or you can use the triangle method. With the triangle method, you use the triangle given below and you cover up the variable you are trying to find. This allows you to know if you need to multiply or divide the remaining variables.

Velocity Triangle: How to use: Cover the variable you are solving for with your hand. The remaining variables will either be multiplied or divided as shown by the image.
Resulting Equations:
velocity = (distance / time)

distance = velocity x time
time = distance / velocity

Watch the given units and the required units carefully. You need to make sure the units match. For instance, if the problem gives you a distance in miles but the final answer is asked for in meters then it will be important to convert before you plug the numbers into the equation.

For example, look at this problem. A commuter train travels from Washington D.C. to Baltimore in 45 minutes. The distance between the two stations is approximately 41 miles. What is the average speed of the train in m/s?

Convert 41 miles to meters:
Convert 45 minutes to seconds:
Plug calculated distance and time into the velocity equation:

Convert 41 miles to meters:

$LaTeX: \frac{41mi}1{}*\frac{1609m}{1mi}=65983.1m$ $\frac{41mi}1{}*\frac{1609m}{1mi}=65983.1m$

Convert 45 minutes to seconds:

$LaTeX: \frac{45min}{1}*\frac{60sec}{1min}=2700sec$ $\frac{45min}{1}*\frac{60sec}{1min}=2700sec$

Plug calculated distance and time into the velocity equation:

$LaTeX: velocity=distance\div time={65983.1m}\div {2700sec}=24.438\frac{m}{s}$ $velocity=distance\div time={65983.1m}\div {2700sec}=24.438\frac{m}{s}$

Check to ensure you have significant digits. Since there are 2 significant digits in each of the given numbers, then the answer should also have 2 significant digits. You should round your final answer to: 24 m/s

Be sure always to include your units with your final answer.

Velocity Practice Problems

What is the velocity of a cheetah that travels north 118.0 meters in 6.0 seconds?

Looking For:

Velocity of cheetah

Solution:

V = d = 118.0 meters = 19.7 m/s

t 6.0 seconds

V = 19.7 m/s North

Given:

Distance = 118.0 meters

Time = 6.0 seconds

Equation:

A bicyclist travels 60.0 kilometers in 3.5 hours towards Atlanta. What is the cyclist's average velocity?

Looking For:

Velocity of bicyclist

Solution:

V = d = 60.0 km = 17 km/hr

t 3.5 hr

V = 17 km/hr towards Atlanta

Given:

Distance = 60.0 kilometers

Time = 3.5 hours

Equation:

How much time would it take for the sound of thunder to travel 1,500 meters if sound travels at a speed of 330 m/sec?

Looking For:

Time for thunder to travel

Solution:

t = d = 1,500 m = 4.55 seconds

v 330m/sec

t = 4.55 seconds

Given:

Distance = 1,500 meters

Velocity = 330 m/sec

Equation:

How far can a person run in 15 minutes if he runs at an average speed of 16 km/hr?

Looking For:

Distance person can run

Solution:

d = v x t = 16 km/hr x .25 hours =

4 km

d = 4 km

Given:

Time = 15 minutes

Velocity = 16 km/hr

Equation:

Formula distance / (velocity x time)

*Must convert 15 minutes to hours in order to get the units the same.

15 minutes x 1 hour = .25 hours

60 minutes

[CC BY 4.0] UNLESS OTHERWISE NOTED | IMAGES: LICENSED AND USED ACCORDING TO TERMS OF SUBSCRIPTION