Time Speed and Distance: Formula & Triangle

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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 ( $m$ ).

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 $(s)$ .

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

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:

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

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.

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

Or in symbols:

$s = v t$

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.

Time Speed and Distance Speed triangle StudySmarter 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 $5 km$ every Sunday. She runs this in $40 \min$ . Work out her speed in $m / s$ , if she can maintain the same speed throughout the run.

Unit conversion

$5 km = 5000 m, 40 \min = 60 \times 40 s = 2400 s$

Time Speed and Distance Speed triangle for calculating speed StudySmarter 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

$Speed = \frac{Distance travelled}{time taken} Speed = \frac{5000 m}{2400 s} = 2.083 m / s$

Calculating Time

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

Time Speed and Distance Speed triangle for calculating time StudySmarter Speed triangle for calculating time, StudySmarter

Unit conversion

$7 km = 7000 m, Speed = 2.083 m / s$

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

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

Converting seconds to minutes

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

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 $8 m / s$ for $25 s$ ?

Time Speed and Distance Speed triangle for calculating distance StudySmarter 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.

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

Sandy will be able to cover a distance of $200 m$ in $25 s$ ! 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: $Speed = \frac{Distance}{Time}, Time = \frac{Distance}{Speed}, Distance = Speed x Time$
The Speed triangle can help you memorize the three 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.
Cover the quantity that you want to measure in the speed triangle and the formula to calculate it will reveal itself.

Flashcards in Time Speed and Distance 6

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Speed is a vector quantity.

False

Distance is a ...

Scalar quantity

The SI unit for speed is ...

m/s

What is the equation for speed?

Distance/Time

Why is speed a scalar quantity?

It has only magnitude

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

450 miles

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Frequently Asked Questions about Time Speed and Distance

What is the meaning of time distance and speed?

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.

How are time distance and speed calculated?

Time distance and speed can be calculated using the following formulae

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

What are the formulas for calculating time distance and speed?

Time distance and speed can be calculated using the following formulae

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

What are the time, speed, and distance triangles?

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.

How does distance and time affect speed?

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.

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Time Speed and Distance

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