Suggested languages for you:
|
|

## All-in-one learning app

• Flashcards
• NotesNotes
• ExplanationsExplanations
• Study Planner
• Textbook solutions

# Time Speed and Distance

Save
Print
Edit

Have you noticed how in car shows they always talk about the time a car takes to reach from zero to$60mph$? They also talk about something called top speed. So, what does it mean when a vehicle is traveling at$100mph$? Can we relate this term with the distance it can cover in a given amount of time? Well, the short answer is yes. In the following article, we will go through the definitions of speed, distance, time and the relation between the three. We will also look at how we can use a triangle to represent the relationship between the three. Finally, we will use a few examples to calculate the speed of different objects.

## Distance speed and time definition

Before we get into the relationship between distance, speed, and time we need to understand what each of these terms means in physics. First, we look at the definition of distance. With it being one of the most commonly used words in the dictionary, most people should know what distance means.

Distance is a measure of the ground covered by an object. The SI unit of distance is the meter ($\mathrm{m}$).

Distance is a scalar quantity. When we talk about the distance covered by an object we are not talking about the direction that the object is traveling. Quantities that have both a magnitude and a direction are called vector quantities.

What about time? How can physics complicate the definition of something as simple as time? Well, as simple as it is it has been one of the most interesting areas of research for scientists like Albert Einstein.

Time is defined as the progression of an event from the past to the present and a future. The SI unit for time is the second$\left(\mathrm{s}\right)$.

Finally, now that we know the definition of distance and time in the context of physics, we can look into how it is used to define one of the most important quantities in the realm of physics, Speed.

Speed refers to the distance travelled by an object in a given time frame.

The SI unit of speed in meters/seconds ($\mathrm{m}/\mathrm{s}$). In the imperial system, we use miles per hour to measure speed. For example, when we say an object is moving at$60\mathrm{mph}$what we mean is that this object will cover a distance of$60\mathrm{miles}$if it continues to move at this rate for the next$1\mathrm{hour}$. Similarly, we can define a speed of$1\mathrm{m}/\mathrm{s}$as the rate at which an object moves when it covers$1\mathrm{meter}$in$1\mathrm{second}$.

## Time speed and distance formula

Let's look at the relationship between distance time and speed. If an object is moving at a uniform speed in a straight line then its speed is given by the following equation:

$\mathrm{Speed}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{time}\mathrm{taken}}$

This simple formula can be rearranged in two ways to calculate time and distance. This is depicted using a speed triangle. The triangle will help you remember the three formulae including the equation above.

$\begin{array}{rcl}\mathrm{Time}& =& \frac{\mathrm{Distance}}{\mathrm{Speed}}\\ \mathrm{Distance}& =& \mathrm{Speed}×\mathrm{Time}\end{array}$

Or in symbols:

$s=vt$

Where$s$is the distance travelled,$v$is the speed and$t$is the time taken to travel the distance.

## Distance speed and time triangle

The above relations can be shown using something called a speed triangle as shown below. This is an easy way to remember the formula. Divide the triangle into three and put the distance D on the top, the speed S in the left box, and the time T in the right box. This triangle will help us remember the different formulas that can be derived from the triangle.

The Speed, distance and time triangle can be used to calculate one of these three variables, StudySmarter

## Time speed and distance calculation steps

Let's look at how we can use the distance speed and time triangle to obtain formulae for each of the variables.

### Calculating Speed

Sandy runs$5\mathrm{km}$every Sunday. She runs this in$40\mathrm{min}$. Work out her speed in$\mathrm{m}/\mathrm{s}$, if she can maintain the same speed throughout the run.

Unit conversion

$5\mathrm{km}=5000\mathrm{m},40\mathrm{min}=60×40\mathrm{s}=2400\mathrm{s}$

Speed triangle for calculating speed, Nidhish-StudySmarter

Now, take the speed triangle and cover the term that you need to calculate. In this case it is speed. if you cover up the speed then the formula will look as follows

$\mathrm{Speed}=\frac{\mathrm{Distance}\mathrm{travelled}}{\mathrm{time}\mathrm{taken}}\phantom{\rule{0ex}{0ex}}\mathrm{Speed}=\frac{5000\mathrm{m}}{2400\mathrm{s}}=2.083\mathrm{m}/\mathrm{s}\phantom{\rule{0ex}{0ex}}$

### Calculating Time

Imagine if Sandy from the above example ran$7\mathrm{km}$maintaining a speed of$2.083\mathrm{m}/\mathrm{s}$. How long would it take for her to complete this distance in hours?

Speed triangle for calculating time, StudySmarter

Unit conversion

$7\mathrm{km}=7000\mathrm{m},\mathrm{Speed}=2.083\mathrm{m}/\mathrm{s}$

Cover the box with time in it. You're now left with the formula distance over speed as follows

$\begin{array}{rcl}\mathrm{Time}& =& \frac{\mathrm{Distance}}{\mathrm{Speed}}\\ & =& \frac{7000\mathrm{m}}{2.083\mathrm{m}/\mathrm{s}}=3360.5\mathrm{s}\end{array}$

Converting seconds to minutes

$3360.5\mathrm{s}=\frac{3360.5\mathrm{s}}{60\mathrm{s}/\mathrm{min}}=56\mathrm{min}$

### Calculating Distance

From the above examples, we know that Sandy likes to run. How much distance could she cover if she ran all out with a speed of$8\mathrm{m}/\mathrm{s}$for$25\mathrm{s}$?

Speed triangle for calculating distance, Nidhish-StudySmarter

Using the speed triangle cover the box that holds the distance. We're now left with the product of speed and time.

$\begin{array}{rcl}\mathrm{Distance}& =& \mathrm{Time}×\mathrm{Speed}\\ & =& 25\mathrm{s}×8\mathrm{m}/\mathrm{s}=200\mathrm{m}\end{array}$

Sandy will be able to cover a distance of$200\mathrm{m}$in$25\mathrm{s}$! Do you think you can outrun her?

## Time Speed and Distance - Key takeaways

• Distance is a measure of the ground covered by an object when it moves without any regard to the direction of motion. Its SI unit is meters
• Time is defined as the progression of an event from the past to the present and a future. Its SI unit is seconds
• Speed refers to the distance travelled by an object in a given time frame.
• The following relations exist between time speed and distance travelled:$\mathrm{Speed}=\frac{\mathrm{Distance}}{\mathrm{Time}},\mathrm{Time}=\frac{\mathrm{Distance}}{\mathrm{Speed}},\mathrm{Distance}=\mathrm{Speed}\mathrm{x}\mathrm{Time}$
• Divide the triangle into three and put the distance D on the top, the speed S in the left box, and the time T in the right box.
• Cover the quantity that you want to measure in the speed triangle and the formula to calculate it will reveal itself.

Time is defined as the progression of an event from the past to the present and from the present to the future. Its SI unit is seconds, Distance is a measure of the ground covered by an object when it moves without any regard to the direction of motion, Its SI unit meters and speed refers to the distance travelled by an object in a given time frame.

Time distance and speed can be calculated using the following formulae

Time = Distance ÷ Speed, Speed= Distance ÷ Time and Distance = Speed × Time

Time distance and speed can be calculated using the following formulae

Time = Distance ÷ Speed, Speed= Distance ÷ Time and Distance = Speed × Time

The relations between time, speed, and distance can be shown using something called a speed triangle. This is an easy way to remember the 3 formulae. Divide the triangle into three and put the distance D on the top, the speed S in the left box, and the time T in the right box.

The larger the distance travelled by a moving object over a given time interval, the faster the moving object. The longer the time it takes for an object to travel a certain distance, the slower the object is moving and so the lower its speed.

## Final Time Speed and Distance Quiz

Question

Speed is a vector quantity.

False

Show question

Question

Distance is a ...

Scalar quantity

Show question

Question

The SI unit for speed is ...

m/s

Show question

Question

What is the equation for speed?

Distance/Time

Show question

Question

What is the speed triangle used for?

The Speed triangle is an easy way to remember the relationship between speed, distance, and time.

Show question

Question

Why is speed a scalar quantity?

It has only magnitude

Show question

Question

Mr. Andrew drives his motorbike for 3 hrs at 150 miles/hr. How far will he travel?

450 miles

Show question

More about Time Speed and Distance
60%

of the users don't pass the Time Speed and Distance quiz! Will you pass the quiz?

Start Quiz

## Study Plan

Be perfectly prepared on time with an individual plan.

## Quizzes

Test your knowledge with gamified quizzes.

## Flashcards

Create and find flashcards in record time.

## Notes

Create beautiful notes faster than ever before.

## Study Sets

Have all your study materials in one place.

## Documents

Upload unlimited documents and save them online.

## Study Analytics

Identify your study strength and weaknesses.

## Weekly Goals

Set individual study goals and earn points reaching them.

## Smart Reminders

Stop procrastinating with our study reminders.

## Rewards

Earn points, unlock badges and level up while studying.

## Magic Marker

Create flashcards in notes completely automatically.

## Smart Formatting

Create the most beautiful study materials using our templates.

Just Signed up?

No, I'll do it now