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Students are commonly asked to determine the distance, speed, or travel time of something given any two variables. These types of problems are quite interesting to solve as it describes real-life situations for many people. For example, a question might say, “ Find the distance a car has travelled in twenty minutes at a constant speed of 50 km /hr. Generally in these problems, we use the distance speed time formula to calculate the desired quantity.

Speed is defined as the rate at which an object moves from one place to another in a given interval of time. It is a scalar quantity as it defines only the magnitude not directions of an object moving. The S.I. unit of speed is m/s.

The speed of a moving object can be calculated as:

Speed = \[\frac{Distance}{Time}\]

Speed can either be uniform or variable.

**Average Speed:** The average speed is the total distance covered by an object in a particular interval of time. For example,

If a moving object covers d₁, d₂, d₃...dₙ with different speed V₁, V₂, V₃ m/s in time t₁, t₂, t₃ respectively, the average speed is calculated as:

Then the average speed of an object is given as:

\[\frac{Total Distance Traveled}{Total Time Taken}=\frac{d_{1},d_{2},d_{3},..d_{n}}{t_{1},t_{2},t_{3}...t_{n}}\]

Relative speed is the speed of a moving object in terms of another.

When two objects are moving in the same direction, then the difference of their speed is termed as relative speed.

When two objects are moving in the same direction, then the sum of their speed is termed as relative speed.

Let us understand the relative speed formula in time and distance with an example.

If two objects are moving in the same direction at x₁ m/s and x₂ m/s, respectively, where x₁ > x₂, then their relative speed is (x₁ - x₂) m/s.

Example,

Consider two objects X and Y separated by a distance of d meters. Suppose, If both X and Y are moving in the same direction at the same time at a speed of x meter per second and y meter per second respectively, then

Relative speed = (X - Y) metre per second

The time required for X to meet Y can be calculated as

If two objects are moving in the different direction at x₁ m/s and x₂ m/s, respectively, where x₁ < x₂, then their relative speed is (x₁ + x₂) m/s.

Example

Consider two objects X and Y separated by a distance of d meters. Suppose, If both X and Y are moving in the same direction at the same time such X moves towards Y at speed of x m/s, and Y moves away from X at a speed of y m/s, where X > Y, then

Relative Speed = (X + Y) metre per second

The time required for X to meet Y can be calculated as

Distance refers to the length of the path covered by an object or person.

You can calculate the distance travelled by an object if you know how long and how fast it moved. The distance travelled by an object or person in terms of speed and time can be calculated as :

Distance = Speed/Time

Time refers to the duration in hours, minutes, or seconds spent to cover a particular distance.

Time taken by a moving object to a cover a certain distance at a given speed is calculated as :

Time = \[\frac{Distance}{Speed}\]

The speed, time, and distance of a moving object can be calculated by using the following formulas of distance speed and time.

Distance Speed Time Formula is given as:

Speed = \[\frac{Distance}{Time}\]

Distance = Speed x Time

Time = \[\frac{Distance}{Speed}\]

Here, we will learn to solve the distance, speed, and time of a moving object by using the formulas of speed time distance

1. A Car Person Travels a Car at a Speed of 50 km Per Hour, How Far Can He Cover in 2.5 Hours?

Solution:

The equation for calculating distance travelled by car, given speed and time, is

Distance = Speed/Time

Substituting the values, we get

D = 50/2.5

D = 125 km

Hence, a car can travel 125 km in 2.5 hours.

2. If a Boy Travels at a Speed of 40 Miles Per Hour. At the Same Speed, How Long Will He Take to Cover the Distance of 160 Miles?

Solution:

The formula to calculate time, when speed and distance are given is:

Time = \[\frac{Distance}{Speed}\]

Time taken by car to cover 160 miles is :

T = \[\frac{160}{40}\]

T = 4 hours

Hence, a boy will take 4 hours to cover a distance of 160 miles at a speed of 40 miles per hour.

3. Two Boys are Running From the Same Place at a Speed of 7 km/ hr and 5 km/hr. Find the Distances Between Them After 20 Minutes Respectively if They Move in the Same Direction.

Solution:

When boys run in the same direction,

Their relative speed = ( 7 - 5) km/ hr = 2 km/ hr.

Time taken by boys = 20 minutes

Distance covered = Speed × Time

D = 20 2060

D = 20 13

D = 6.6 km

From this discussion, we have concluded that,

If two moving bodies are moving at the same speed, the distance travelled by them is directly proportional to the time of travel i.e when speed is constant.

If two moving bodies move for the same time, the distance travelled by them is directly proportional to the time of travel i.e when time is constant.

If two moving bodies are moving at the same distance, their travel of time is inversely proportional to speed i.e when the distance is constant.

FAQ (Frequently Asked Questions)

1. Who Discovered the Speed Formula?

Ans: Galileo Galilei ( Italian Physicist) is credited with being the first to measure the speed of a moving object concerning the time taken and distance covered. He defined speed as the distance covered by an object or person per unit of time.

2. What is the Formula of Speed Distance Time?

Ans: The formula of speed time distance time can be rearranged as shown below.

Speed = Distance / Time

Distance = Speed × Time

Time = Distance / SpeedDistanceSpeed

3. What is Known as Instantaneous Speed?

Ans: Instantaneous speed is the speed of a moving object at a specific point of time. For example, a car is presently travelling at 60 km/ hr, but it may speed up or slow down in the next couple of hours.