Speed Time Distance Formula
Last Updated : 28 Feb, 2024
Speed, Distance, and Time are the three most important physical quantities which are of utmost importance in Kinematics. The three quantities Speed, Distance, and Time are related to each other through a unique relation called as Time Speed Distance Formula abbreviated as TSD Formula. The Speed Distance Time formula will help us to calculate the speed, time taken, and distance travelled by a body under different conditions when any one of them is missing.
The Time Speed Distance formula will also help us to calculate the average speed for the journey and many more parameters. In this article, we will about what is speed, what is distance, and what is time, and also learn Speed Distance Time Formula to calculate the values of these three parameters under different conditions.
What is Distance?
Distance is basically the length of the path between two points on a plane. It is dimensionally equal to length which is one of the seven fundamental quantities. Hence the SI unit of distance is a meter 'm' but smaller units are centimetres (cm) and larger units are kilometres (km), Miles, etc. The other units of distance are light years which is used to measure the distance between two astronomical bodies. 1 light year is equal to 9.461 ⨯ 1012 km. Nautical Mile is also a unit of distance that is used to measure distance in marine and air navigation based on Earth's latitude and longitude. 1 Nautical Mile is equal to 1.852 km.
The distance may not be given in the desired unit, hence one needs to learn the conversion of distance from one unit to other units. For Example, if you need to convert Km to m, multiply km by 1000, and if want to convert m to km, divide by 1000.
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Distance vs Displacement
Distance and Displacement are dimensionally the same quantity with some basic differences. They have the same unit i.e. m or km. The difference between Distance and Displacement is tabulated below:
|
Distance is the actual total path length between two points on the plane. | Displacement is the shortest path length between the two points on the plane. |
Distance is a scalar quantity | Displacement is a vector quantity |
Distance is always positive | Displacement can be positive, negative, or zero depending on the direction |
Read more about Distance and Displacement.
What is Time?
Time is basically the advancement of incidents. Time is one of the most fundamental quantities out of the seven fundamental quantities defined by science. Time is recorded on Earth with respect to the rotation and revolution of Earth. Early man used to observe the time with the position of the sun in the sky. Later on, sand clocks developed which were followed by mechanical clocks and so on. Time is dimensionally represented as [T]. The SI unit of Time is Second(s). The larger units of Time are minutes and hours. In an hour there are 60 minutes and there are 60 seconds in a minute. A day consists of 24 hours.
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What is Speed?
Speed is the rate of covering distance per unit of time. Speed basically tells how fast or slow a body is travelling. Mathematically, Speed is given as the ratio of Distance and Time. Speed is not a fundamental quantity instead it is a derived quantity. Since speed is the ratio of distance and time, the unit of speed is m/s which is the ratio of the SI unit of Distance and Time. The larger units of speed are Km/h and m/min. The dimensional formula of speed is [LT-1]
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Speed vs Velocity
Speed is the rate of covering distance irrespective of direction while velocity is the rate of covering distance in a particular direction. Speed and Velocity are the same quantities in terms of physical dimension but they are different in their nature. The unit of both Speed and Velocity is m/s. The difference between speed and velocity is tabulated below:
|
Speed is the rate of covering distance irrespective of any direction. | Velocity is the rate of covering the distance in a specific direction |
Speed is a scalar quantity | Velocity is a vector quantity |
Speed changes only with the change in magnitude | Velocity changes with changes in either magnitude or direction |
Speed is given as Distance/Time | Velocity is given as Displacement/Time |
| Speed is always positive | Velocity can be positive or negative depending upon direction. |
Read more about Speed and Velocity.
Time Speed and Distance Formula
The three physical quantities time, speed, and distance are related to each other through a formula called Time Speed Distance Formula. The Speed Distance Time Formula is given as:
Speed = Distance/Time
OR
s = d/t
Where,
- s is speed or velocity,
- d is Distance, and
- t is Time.
Relationship between Speed, Distance and Time
Based on the above formula, the relationship between Speed, Distance, and Time is discussed below:
- Speed is the rate of covering distance per unit of time, hence Speed = Distance/Time. The SI unit of speed is m/s.
- Time is the duration in which a particular distance is covered travelling at a given speed, thus Time = Distance/Speed. The SI unit of Time is second(s).
- Distance is the path covered by a body moving at a given speed for a given period of time. Hence, the formula for distance is given as Distance = Speed ⨯ Time. The unit of distance is m or km.
- Distance and Time are directly proportional to each other. It means if a body is travelling at a given speed then as the time increases, distance cover will also increase.
- Distance and Speed are directly proportional to each other. It means in a certain duration of time, a body travelling at a larger speed will travel a larger distance.
- Speed and Time are inversely related to each other. It means, the larger the speed lower will be the time taken to cover a specific distance.
Average Speed
Average Speed is defined as the ratio of the total distance travelled in the total duration of time. In real life scenario, the speed doesn't remain the same, hence we can't tell the speed with which we completed our journey. So for this purpose, the concept of average speed was introduced. Its unit is the same as that of speed and it is also a scalar quantity.
Average Speed Formula
The average speed formula is given as
Average Speed = Total Distance Travelled/Total Time Taken
OR
Average Speed = d1 + d2 + d3 + .... + dn/ t1 + t2 + t3 + ... + tn
Where,
- d1, d2 . . . dn are distances travelled, and
- t1, t2 . . . tn is the time taken during the travelled distance.
Learn more about Average Speed Formula.
Relative Speed Formula
When two bodies are in motion then the speed of one body with respect to another body is called Relative Speed. The Relative Speed Formula for different cases is mentioned below:
Relative Speed Between Trains
In this heading, we will learn Relative Speed between trains travelling in the same and opposite directions. It should be noted that when two crosses each other whether in the same or opposite direction, the total distance is given by summation of the length of two trains.
Relative Speed Between Trains Travelling in the Same Direction: In this case, the relative speed between is given by the summation of speeds of individual trains. Hence, the time taken to cross two trains travelling in the same direction is given by
Time taken by two trains traveling in same direction = Sum of length of two trains/Sum of speed of two trains
Relative Speed Between Trains Travelling in Opposite Directions: In this case, the relative speed is given by the difference of speed of two trains. Hence, the time taken to cross two trains travelling in the opposite direction given by
Time taken by two trains traveling in opposite direction = Sum of length of two trains/Difference of speed of two trains
Relative Speed Between Man and Train
For a man running parallel to a moving train, the relative speed is given by the sum of the speed of man and the train if both are running in the same direction, and the relative speed is given as the difference between the speed of man and a train if they are moving opposite to each other. It should be noted that the distance to be crossed is equal to the length of the train only.
Time taken to cross each other when man is running in train's direction = Length of train/Sum of Speed of Train and Man
Time taken when train and man running in opposite to each other = Length of train/Difference of Speed of Train and Man
Learn more about Relative Motion.
Unit Conversion
The three quantities, Speed, Distance and Time may or may not be in standard units or you may be asked to calculate a problem in a particular unit. Hence for this purpose, we need to learn unit conversion.
Unit Conversion Length (Distance)
For this, the relation between some units should be memorized.
- 1 km = 1000m
- 1m = 100cm
- 1m = 1000mm
- 1cm = 10mm
- 1mile = 1.6km
- 1nautical mile = 1.852km
The above relation must be remembered to convert the units. To convert units from larger units to smaller units we multiply and to convert from smaller units to larger units we divide. For Example, if we want to convert 2 km into m we will multiply 2 by 1000 as 1 km = 1000 m and we are converting from km to m. Hence, 2 km = 2 ⨯ 1000 m = 2000 m. If we have to convert m to km i.e. from a smaller unit to a larger unit we divide. Hence, 500 m = 500/1000 km = 0.5km
Learn more about the System of Units.
Time Unit Conversion
For time unit conversion we need to memorize the following relation between units of time
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- 1 hour = 3600 seconds
- 1 day = 24 hours
Here, also we perform the multiplication for conversion from a larger unit to a unit and division from a larger unit to a smaller unit. For Example, 2 hr = 2 ⨯ 60 = 120 min and 120 min = 120/60 = 2 hours
Unit Conversion Speed
The SI unit of speed is m/s. We also use km/h as a unit of speed. If the speed is given in m/s multiply it by 18/5 to convert it into km/h and if the speed is given in km/h multiply by 5/18 to convert it into m/s.
In short,
- m/s ⨯ 18/5 = km/h
- km/h ⨯ 5/18 = m/s
Read More,
Sample Problems on Speed Time and Distance Formula
Problem 1: Calculate the distance travelled by truck with a speed of 6 km/hr in 1 hour.
Solution:
Given: s = 6 km/hr. , t = 1 hour
The distance speed time formula states that: s = d/t
⇒ d = s × t
= 6 km/hr × 1 hr.
= 6 km
Problem 2: A car has covered 90 km in 2 hours. What is its speed?
Solution:
Given: d = 90 km , t = 2 hours
The distance speed time formula states that: s = d/t
= 90 km/ 2 hours
= 45 km/hr
Problem 3: Find the time taken by a cyclist to cover 4 km at a speed of 10 km/hr.
Solution:
Given: d = 4 km, s = 10 km/hr.
The distance speed time formula states that: s = d/t
⇒ t = d/s
= 4 km/ 10 km/hr
= 0.4 hr = 24 minutes
Problem 4: Calculate the distance travelled by truck with a speed of 3 km/hr in 8 hours.
Solution:
Given: s = 3 km/hr. , t = 8 hour
The distance speed time formula states that: s = d/t
⇒ d = s × t
= 3 km/hr × 8 hr.
= 24 km
Problem 5: Calculate the distance travelled by truck with a speed of 18 km/hr in 8 hours.
Solution:
Given: s = 18 km/hr, t = 8 hours
The distance speed time formula states that: s = d/t
⇒ d = s × t
= 18km/hr × 8 hr.
= 144 km
Problem 6: Imagine the distance is doubled and the time is halved, what will be the new speed?
Solution:
Suppose, the speed was "s" earlier, time was "t" earlier, distance was "d".
s = d/t ⇢ (1)
New distance = 2d
New time = t/2
New speed = s' = 2d/(t/2)
s' = 4d/t
s' = 4s
The new speed will be 4 times the old speed.
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