Time, Speed and Distance Concepts

Understanding the Concepts of Time, Speed and Distance

The fundamental concepts of Time, Speed and Distance can be properly represented using the diagram below.

Let us understand the meaning of these concepts/terms one by one

1. Speed

Speed is a motion concept that describes how slowly or swiftly an item moves. Speed is defined as the distance divided by Time. Speed is measured in m/s, km/hr

Speed = Distance / Time

2. Time

Time can be defined in physics by its unit of measurement - time is the reading on a clock. In classical, non-relativistic physics, it is a scalar quantity and measured in seconds (s), minutes (min), and hours (hr)

3. Distance

Distance refers to an object's total movement, independent of direction. The amount of area covered by an item, independent of its beginning or finishing location, can be described as distance. It is measured in Metre (m), kilometre (km), miles, and feet.

Concept of Proportionality

To address problems faster, we must also comprehend the concept of proportionality between these elements.

1. Direct Proportion
2. Inverse Proportion

1. Direct Proportion

The term 'direct proportion' refers to the direct link between two quantities. When one quantity rises, the other rises as well, and vice-versa. As a result, a direct proportion is expressed as y ∝ x.

For Example

When the speed of a car is raised, it travels a greater distance in a given amount of time.

• Time & Distance are directly proportional
• Speed & Distance are directly proportional

2. Inverse Proportion

Inverse proportion explains the connection between two quantities in which one rises while the other falls and vice-versa. As a result, an inverse proportion is expressed as y ∝ 1/x.

For Example

If the speed of a vehicle is increased, it will cover a fixed distance in less time.

• Time & Speed are Inversely proportional

Subconcepts of Time, Speed and Distance

Subconcepts of Time, Speed, and Distance include:

1. Unit Conversion
2. Average Speed
3. Concept of Relative Speed
4. Effective Speed Concepts

1. Unit Conversion

We are required to convert all the parameters in a single unit in some of the Time Speed and Distance problems where speed is given in one unit and distance is provided in another.

The following conversion formula can assist you in accomplishing this.

Speed conversion from km/hr to m/s and vice-versa

• 1 kilometre equals 1000 m , and 1 hour equals 3600 seconds.

Therefore, 1 km/hr = 1000m/3600s = 5/18 m/s.

So, to translate the speed from kmph to m/s

• Multiply the given speed with 5/18

And to convert the speed from m/s to kmph

• Multiply the given speed with 18/5.

2. Average Speed

The ratio of total distance travelled to total time taken is described as average speed.

Total distance / Total time taken = Average speed

Shortcut formula:

We can use the following shortcut formula to get the average speed when two different speeds are provided but the distance travelled in both segments is identical.

Average speed = 2xy/(x+y)

where x and y represents the two speeds.

Example Problem

A person travels from X to Y at a speed of 20 kmph and returns at a speed of 30 kmph. What is his average speed for the entire trip?

We can utilise the aforementioned shorthand calculation:

Average Speed: 2xy/(x+y)

⇒ 22030/ (20+30)

The answer is 24 kmph.

3. Concept of Relative Speed (Problems on Trains)

This concept is frequently used in train-related problems The concept of relative speeds can be applied when two things are heading toward each other or in the same direction, one after the other.

In terms of relative speed,

• If two objects are moving from opposing directions towards each other, always add their speeds.

• When two objects are moving in the same direction, following each other, always subtract their speeds.

We'll learn more about this on the Problems on Trains concepts.

4. Effective Speed Concepts (Boats & Streams)

This concept is often used in boats and streams. The effective speed is the net speed at which the thing moves in relation to the speed of the other moving object.

Downstream or Down Hill refers to when both objects are flowing in the same direction, either with the water or with gravity, as when descending down a staircase.

Likewise, if both items are travelling in opposing directions, or moving against the flow of water or against gravity, such as climbing a flight of stairs, it is referred to as upstream or uphill.

This can be effectively summarised using the formula,

• Downstream Speed = Speed of the Boat + Speed of the Stream/Current/Water

• Upstream Speed = Speed of the Boat - Speed of the Stream/Current/Water

We'll learn more about this on the Boats and Streams concepts.