# How to Find Speed

Two Parts:Understanding SpeedUsing the Formula

Most problems about speed ask you to find either the average speed or velocity. While those terms are frequently tossed around interchangeably, they are different. Velocity is a vector quantity that takes direction into account while speed is scalar and defined only by the magnitude.^{[1]} In other words, when talking about velocity you talk about both the speed and the direction the object is traveling. Speed is only the absolute value of the rate at which the object is traveling. The speed you are going at any given moment is different from the average speed, however, the equation to calculate both is the same.

## Steps

### Part 1 Understanding Speed

- 1
**Define speed.**The speed of an object is the total distance traveled divided by the time it took to travel that distance.^{[2]}Unlike a vector which is defined by having both a magnitude and direction, such as velocity, speed only has a magnitude.^{[3]}- Magnitude is the size or amount of the term. Another way to think about magnitude is how far away the term is from zero.
^{[4]}For example, if a car is moving at 15 miles per hour, it is 15 away from zero and therefore has a magnitude of 15. - The formula to calculate speed is
*speed = total distance/total time*

- Magnitude is the size or amount of the term. Another way to think about magnitude is how far away the term is from zero.
- 2
**Understand instantaneous speed.**Instantaneous speed is the rate at which an object is moving in a given moment. Speed is expressed as the ratio of distance to time. When traveling in a car, your instantaneous speed is what the speedometer reads at any point in time. It is the rate you are traveling at that moment.- Common units for speed include miles per hour (mph) and kilometers per hour (kph).

- 3
**Understand average speed.**Average speed is the total distance traveled for a given amount of time.^{[5]}The formula for both average and instantaneous speed is the same, but average speed takes into account the whole trip, while instantaneous speed is only for a specific moment of time.^{[6]}- The example used in the following steps will calculate average speed.

### Part 2 Using the Formula

- 1
**Write down the formula.**The first step to solving any problem is writing down the formula needed to solve it. Start by writing the formula and determining the variables needed to solve it.*speed = total distance/total time*- To solve, identify the total distance and the total time associated with the problem.

- 2
**Calculate the total distance traveled.**Speed problems will usually give you the amount of distance someone travels over a period of time. Identify all the distances traveled in the problem. It can be helpful to circle the distances so you don’t miss one. Add these distances together for total distance traveled.- If you’re calculating the average speed of a road trip, use an online tool to provide route information and mileage.
- Example: Keri travels 7 miles (11 km) in 10 minutes, takes a break, and then makes the return trip in 20 minutes. What was her average speed?
- The total distance traveled in this problem is 7 miles (11 km) + 7 miles (11 km) = 14 miles (23 km).

- 3
**Calculate the total amount of time traveled.**The problem will also tell you the various times it took to travel each distance. Identify all of the times and add them together to find the total time it took to travel all of the distances.- For our example, the first trip took 10 minutes and the second trip took 20 minutes, so 10 + 20 = 30 minutes total travel time.

- 4
**Divide the total distance by the total time traveled.**In order to finish the calculation you will take the total distance traveled and divide it by the amount of time it took to travel that distance.- Example: 14 miles/30 minutes = 0.46 miles/minute or 28 miles/hour.
- Make sure to include the appropriate units with your answer.

- 5
**Convert to miles per hour, if necessary.**Sometimes you will be asked to convert your answer from the given units to miles per hour. To convert from miles per minute to miles per hour simply multiply by the conversion factor 60 min/1 hr. To convert from kilometers per hour to miles per hour, multiply by the conversion factor 0.62 miles/1 kilometer.- For example: (0.46 miles/min) * (60 min/1hr) = 28 miles/hr
- For example: (10 km/1hr) * (0.62 miles/1 km) = 6.2 miles/hr

## Tips

- Make sure to pay attention to the directions or clarify with your teacher to determine if you need to take direction into account when solving speed-related problems.

## Sources and Citations

- ↑ http://www.physicsclassroom.com/class/1DKin/Lesson-1/Speed-and-Velocity
- ↑ http://study.com/academy/lesson/calculating-average-speed-formula-practice-problems.html
- ↑ https://www.mathsisfun.com/definitions/vector.html
- ↑ https://www.mathsisfun.com/definitions/vector.html
- ↑ http://www.physicsclassroom.com/mmedia/kinema/trip.cfm
- ↑ http://study.com/academy/lesson/calculating-average-speed-formula-practice-problems.html

## Article Info

Categories: Classical Mechanics