Time Speed and Distance

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 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.

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.

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.

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

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

Calculating Time

Calculating Distance