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Distance Formula Physics

We all travel to some area or place on a daily basis and during this travel, we cover some area known as distance. But, from the point of view of the physics distance is something that includes many factors. Furthermore, in this topic, we will discuss distance, what is the distance formula, its derivation and solved example.

what is the distance formula

                                                                                                                                                    Source: YouTube

Distance

It refers to the numerical measurement of how far an object is from a particular place. Also, in physics, it may refer to the physical length or evaluation based on some criteria. Furthermore, a distance from X to Y is exchangeable with distance from Y to X.

Besides, we calculate the distance in physics by keeping in mind various factors like the speed and time to cover a specific distance. Moreover, speed is the measure of how quickly an object or body travels from one place to another.

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What is the Distance Formula

As discussed earlier the distance formula is the combination of distance, speed, and time. Also, we can find any one of them by interchanging the formula if two figures are known. Besides, this can be understood in a better sense by seeing it in formula form.

For speed

Speed = \(\frac{distance}{time}\)

s = \(\frac{d}{t}\)

For time

Time = \(\frac{distance}{speed}\)

t = \(\frac{d}{s}\)

For distance

Distance = speed × time

d = s × t

Derivation of all the Formulas

d = refers to the distance traveled by body or object in meters (m)
s = refers to the speed of the object or body in meter per second (m/s)
t = refers to the time consumed by object or body to cover the distance in seconds (s)

Solved Example on Distance Formula

Example 1

Suppose a dog runs from one end of the street to another end of the street and the street is 80.0 meters across. Moreover, the takes 16.0 seconds to cross reach the end of the street. Now, calculate the speed of the dog?

Solution:

As we discussed earlier the distance formula can be interchanged to find the speed of the body or object.
So, the distance and time is present in the question that is 80.0 m and 16.0 s respectively. Now, put these values in the question

Speed = \(\frac{distance}{time}\)

Speed = \(\frac{d}{t}\)

S = \(\frac{80.0 m}{16.0 s}\)

S = 5.0 m/s

So, the speed of the dog will be 5 m/s.

Example 2

Now, in another situation, a golf cart driver is driving the golf cart that has a maximum speed of 27.0 km/h. Furthermore, the driver drives the car for 10.0 minutes. So, calculate the distance covered by the golf cart with its top speed in 10.0 minutes?

Solution:

For solving this problem first of all we need to convert the speed from km/h to m/s and time from minutes to seconds.
Calculating speed

s = 27.0 km/h

s = 27.0 ×\(\frac {km}{h}\) × \(\frac {1000 m}{1 km}\) × \(\frac {1 h}{60 min}\) × \(\frac {1 min}{60 s}\)

So, s = 7.50 m/s

Calculating time

t = 10.0 min

t = 10.0 min × \(\frac {60 s}{1 min}\)

So, t = 600 s

Now, we have the speed and time of the golf cart in m/s and s respectively. Hence, we put the values in the distance formula to calculate the distance covered by the cart.

d = s × t
d = (7.50 m/s) (600 s)
d = 7.50 × 600
d = 4500 m

So, the golf cart will cover a distance of 4500 m in 10 minutes at the speed of 27 km/h.

Or we can say that it will cover a distance of 4.5 km in 10 minutes.

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