**Definition of Distance** – Distance is a numerical measure that shows how far the position of an object is from another object. In the field of physics or in the everyday sense, distance can refer to the length (physically) between two positions, or an estimate based on certain criteria (for example the distance traveled between Jakarta-Bandung).

## Overview and Definitions

### 1. Physical Distance

A non-general definition of distance can be useful for modeling certain physical situations, but is also used in pure mathematics:

In the picture above, the Euclidean distance between the two points is indicated in the green line. The red, blue, and yellow lines represent Manhattan’s distance between the same two points

- “Manhattan distance” is a squared distance, defined as the number of blocks (north, south, east, or west) that a taxi must travel to reach its destination, on several New York City streets.
- The “chessboard distance”, formally called the Chebyshev distance, is the minimum number of moves the king must make on the chessboard, to get to another square.

The measure of distance in cosmology is more complicated because it is influenced by the expansion factor of the universe, and by the effects explained by the theory of relativity (such as the contraction of the length of moving objects).

### 2. Theoretical Distance

The definition of “distance” is also used as an analogy to measure two non-physical objects in a certain way. In the field of computer science, there is a notation “editing distance” between two lists ( *string* ). For example, the words “makan” and “mamakam” which only differ by one letter, are closer than the words “makan” and “malam” which have a difference of two letters. This concept is used in code theory and in spell checkers. Mathematically, distance can be defined in several ways:

- Levenshtein distance.
- Hamming distance.
- Lee distance.
- Jaro-Winkler distance.

In mathematics, a metric space is a collection in which the distance between the members of the collection is defined. In this way, many types of “distance” can be calculated, such as graph traversal, comparison of distributions and curves, and non-general definitions of “space” (for example folds and reflections).

Distance notation in graph theory is used to describe social networks, for example the Erdős number or the Bacon number—a number that indicates how distant a person’s collaborative relationship is with mathematician Paul Erdős and with actor Kevin Bacon.

In psychology, human geography, and social science, distance is often interpreted not as an objective measure, but as a subjective experience.

## Distance vs Directed Distance and Displacement

Both distance and displacement both measure the movement of an object. Distance is a scalar quantity while displacement is a vector quantity with magnitude and direction. The distance between the two points cannot be negative. On the other hand, directional caraks do not measure movement; it measures the position of a point from a reference point, and is expressed in vector form.

The distance traveled by a vehicle (for example as recorded by an odometer), person, animal, or object along a curved path from point A to point B should be distinguished from the straight line distance from A to B, because in general the straight line distance is not equal to distance traveled, except for travel in a straight line.

### 1. Directed Distance

The directed distance along a curved path is not a vector and is represented by a segment of the curved line determined by the end points A and B, with some specific information that indicates the sense (or direction) of ideal or real motion from one end point of the path to another. For example, just giving A and B as two point labels can show meaning, if the sequence (A, B) implies that A is the starting point.

### 2. Transfer

Displacement is a special case of directed distance defined in mechanics. Directed distance is called displacement if the crossing between point A and B is a straight line (the shortest distance between A and B).

**Distance Formula in Physics with Examples**

The fact is that in physics, distance is the length of the path traveled by an object in a certain period of time. For example, the distance from point A to point B. The same goes for the distance between point A, point B, point C and point D.

An object that starts from point A will go to point D then passes through point B and point C. So the length of the passage from point A to D is the distance traveled by the object. The distance traveled by the object is AB+BC+CD.

In physics, distance has a symbol (s). The symbol is widely used in Indonesia. Different from foreign countries, distance is often with the symbol (d) or distance.

While the unit of distance according to the International System of Units or SI is meters (m). Because distance is a quantity of length, then distance enters the category as a basic quantity. Similarly, this distance includes a scalar quantity and is expressed with a value or number without having a direction.

Distance in physics is also related to the amount of speed, either regular straight motion without acceleration or regular linear motion with speed. The distance formula related to quantity can produce the formula s= vt (distance formula on GLB) or s: v0 . t ± 1/2 a . t2 is the distance formula on GLBB.

For s is the distance (m), t is the time (s), v0 is the initial speed (m/s), v is the velocity and a is the acceleration (m/s²). To calculate time, distance is divided by speed, while calculating speed is distance divided by time.

## Examples of Speed Distance and Time Questions

After knowing the formulas for speed, distance and time above, here are sample questions for better understanding.

1. A car drives at a constant speed. In 3 hours, the car traveled a distance of 210 km. How fast is the car?

A. 80 km/h

B. 70 km/

h C. 72 km/h

D. 82 km/h

E. 76 km/h

Answer: B

Discussion with the speed formula

Distance (S)= 210 km

Time (t)= 3 hours

So, it can be calculated with the formula v= S/t, that is v= 210 km/3 hours v= 70 km/hour

From the calculation using the formula above, the car’s speed is 70 km/h

2. A vehicle travels a distance of 600 meters for 5 minutes, then for the next 10 minutes it travels a distance of 900 meters. After that, the last 750 meters travel time is 15 minutes. The average speed of the vehicle is…

A. 70 meters/minute

B. 750 meters/minute

C. 75 meters/minute

D. 75 km/minute

E. 7.5 meters/minute

Answer: C

Discussion:

S total = 600+900+750= 2250 meters

t total= 5+10+15=30 minutes

So it can be calculated with the formula

v = ∆x / ∆t, namely v= 2250 meters/30 minutes

v= 75 meters/ minute

From the calculation using the formula above, the average speed of the car is 75 meters/minute

3. A car drives at a constant speed. Based on the speedometer, the speed of the car is 90 km/h, for 12 minutes. So, what is the distance traveled during the time interval?

A. 12 km

B. 15 km

C. 14 km

D. 18 km

E. 16 km

Answer: D

Discussion:

v= 90 km/hour = 25 m/second

t= 12 minutes = 720 seconds

So it can be calculated with the formula S = vxt, namely

S= 25 m/second x 720 seconds

S= 18,000 meters = 18 km

From the calculation using the formula above, the result of the distance traveled by the car is 18 km.

4. A truck drives at a speed of 70 km/hour. The truck will travel a distance of 140 km. So, how long does it take the truck to reach its destination?

A. 1 hour 15 minutes

B. 1 hour 30 minutes

C. 2 hours

D. 2 hours 25 minutes

E. 3 hours

Answer: C

Discussion with the speed formula

S= 140 km

v= 70 km/h

So it can be calculated with the formula t = S/v, that is

t= 140 km/70 km/h

t= 2

From the calculation with the formula above, the result of the time required for the truck is 2 hours.

5. Alia drives the car from home to the office, which is about 30 km away and takes 2 hours on the way. So what is the speed of the doni car?

Known:

s = 30 km

t = 2 hours

Asked: v

Answered:

V = s/t

V = 30 km/2 hours

V = 15 km/hour

So, the speed of Alia’s car is 15 km/hour.

6. Surya walks at an average speed of 2 meters per second. So, how far did Surya travel after walking for 2 hours?

Known:

v = 2 meters/second

t = 2 hours = 2 x 60 x 60 = 7200 seconds.

Asked: s

Answered:

s = vxt

s = 2 meters/second x 7200 seconds

s = 14,400 meters = 14.4 km

So, the distance traveled by Surya after walking for 2 hours is 14.4 km.

7. An airplane flies at a speed of 500 km/hour. How long does it take for him to fly from city A to city B when the distance between the two cities is 1,500 kilometers?

Known:

s = 1,500 km

v = 500 km/h

Asked: t from city A to city B

Answered:

t = s/v

t = 1500 km/500 km/h

t = 3 hours

So, the time it takes the plane to fly city A to city B is 3 hours.

8. Wildan drove a car from city A to city B which is about 20 km away for 2 hours and continued the journey 40 km to city C for 3 hours. What is the average speed of Wildan’s car?

Known:

s2-s1 = 40 km – 20 km = 20 km

t2 – t1 = 3 hours – 2 hours = 1 hour

Asked: average speed

Answered:

v = (s2 – s1) / (t2 – t1) = 20 km /hour

So, the average speed traveled by Wildan’s car is 20 km/hour.

9. The distance between Yogyakarta and Magelang is 195 km. If traveled by car at a speed of 65 km/hour. How much time does it take to travel that distance?

Answer: Known: s = 195 km; v = 65 km/h.

Asked: Time or t. t = s ÷ vt = 195 ÷ 65 t = 3

So, the time required to travel the distance from Yogyakarta-Magelang is 3 hours.

10. A fast runner moves in a straight line in 5 seconds. It can travel a distance of 40 meters. The average speed of the runner is…

Answer:

Known: Δs = 40 m, Δt = 5 s. v = Δs/Δt v = 40/5 = 8 m/s So, the average speed of the runner is 8 m/s.

11. An athletic runner is able to cover a distance of 200 meters in a span of 25 seconds. What is the average speed of the runner?

Answer:

Distance traveled = 200 m

Travel time = 25 seconds

Average speed = 200/25 = 8 m/second.

12. A vespa motor covers a distance of 110 kilometers in a period of 2 hours. what is the average speed of the vespa motor.

Answer:

Distance traveled = 110 km

Travel time = 2 hours

Average speed = 110/2 = 55 km/hour.

13. Doni drives his car from home to the office which is about 25 km away and takes 2 hours on the way. So what is the total average speed of the car?

Answer:

Known:

S = 25 km

t = 2 hours

Asked:

average speed (v) ….. ?

Answered:

V = S / t

V = 25 km / 2 hours

V = 12.5 km/hour

So, the speed of the car is 12.5 km/hour.

14. At the time Dono ran it was estimated at an average speed of 1.5 meters per second. So, calculate the total distance traveled by Doni after 2 hours of travel?

Answer :

Known:

v = 1.5 meters/second

t = 2 hours = 2 x 60 x 60 = 7200 seconds.

Asked:

So how much distance can Doni cover after 2 hours of walking (s)?

Answered:

s = vxt

s = 1.5 meters/second x 7200 seconds

s = 10800 meters = 10.8 km

So, the distance traveled by Doni after 2 hours of walking is 10.8 km.

15. There is a plane that is estimated at a speed of 500 km/hour. So, how much time does the plane need to fly from Bandar Lampung to Bandung when the distance between the two cities is 1400 kilometers?

Answer:

Known:

S = 1400 km

v = 500 km/h

Asked:

Do you know the time it takes to fly from Bandar Lampung to Bandung (t)?

Answered:

t = s / t

t = 1400 km / 500 km/h

So, the time it takes an Indonesian Garuda plane to fly from Bandar Lampung to Bandung is 2 hours 48 minutes.

16. Vishal pedals a bicycle with a speed of 2 m/s. So how long does Vishal need to travel 100 meters?

Answer:

Known:

v = 2 m/s

s = 120 m

Asked t ….?

Solution:

t = s / v

t = 100 / 2

t = 50 seconds

So, time taken by vishal is 50 seconds

17. It is known that Ilham rides a motorcycle by traveling a distance of 100 meters in 25 seconds. So what is the speed of Ilham’s motors?

Answer:

Known:

s = 100 m

t = 25 s

Asked v ….?

Solution:

v = s / t

v = 100 / 25

v = 4 m/s

So, the speed of Vishal’s motor is 4 m/s

18. When it is known that the distance X – Y is 33 km. Then a younger brother leaves from X at 09.00 with a speed of 6 km per hour. And his sister is estimated to depart from B at 09.00 at a speed of 5 km per hour. What time will the sister and brother meet?

Discussion:

Use the formula to calculate the distance:

s = v . t

Sister Distance + Sister Distance = 33 km

6 km . t + 5 km. t = 33 km

11 t = 33

t = 3 hours

The time they will meet = 09.00 + 3 hours = 12.00

So, Brother and Sister will meet at 12.00

19. Distance Bekasi–Jakarta 60 km. Angga left for Jakarta by bicycle at 07.30. The average speed figure is 40 km/hour.

Calculate:

a. How much travel time does Angga need to get to Jakarta?

b. What time does Angga arrive in Jakarta?

Answer:

a. we use the Formula to calculate travel time is t=s/v or

= Distance : speed

= 60 km : 40 km/hour

= 1.5 hours

So how much time is needed to travel the distance Bekasi-Jakarta is

1.5 hours = 1 hour 30 minutes.

b. Angga’s arrival in Jakarta = Departure time + travel time

= 07.30 + 01.30

= 09.00

So, Angga arrived in Jakarta at 09.00

20. Karno drives a car with an average speed of 60 km/hour. From Jakarta to the city of Bandung he left at 04:00. When Karno arrived in the city of Bandung at 07.00. How many kilometers has Karno traveled?

Answer:

Explanation of the mileage formula s=vxt

Travel time and = later arrival time – departure time

= 07.00 – 04.00

= 3 hours

Distance traveled = speed X time

= 60 km/hour X 3 hours

= 180 km

So Karno has traveled a distance of 180 km

21. The distance between Jakarta and Bogor is 60 km. Rossa left for Bogor by motorbike at 07.30. Rossa’s average speed is 40 km/h.

Questions:

a. How long does it take Rossa to get to Bogor?

b. What time did Ross arrive in Bogor?

Answer:

a. The formula for calculating travel time is t=s/v or

= Distance : speed

= 60 km : 40 km/hour

= 1.5 hours

So Rossi needs time to travel the distance from Jakarta to Bogor that is.

1.5 hours = 1 hour 30 minutes.

b. Arriving in Bogor = Departure time + then travel time

= 07.30 + 01.30

= 09.00

So Rossa arrived in Bogor at