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Speed, distance and time are three important variables in the field of physics. Speed is a concept of motion that determines how fast or slow an object is moving from one point to another. Speed is defined as the distance travelled in unit time. When time is constant, distance is directly proportional to speed and velocity. The length of the space between two points is considered the Distance. And time is a fundamental physical quantity which defines the sequence and duration of events.
The various units of Speed, Distance and Time are:
- Time: seconds(s), minutes (min), hours (hr)
- Distance: (meters (m), kilometers (km), miles, feet
- Speed: m/s, km/hr
This means that if Distance = km and Time = hr, then for Speed, we can say, Speed = Distance/ Time (wherein the units of Speed are km/ hr).
Read More: Motion in a Straight Line
| Table of Content |
Key Terms: Speed, Time, Distance, Motion, Acceleration, Average Speed, Relative Speed, Variables, Relative Speed, Velocity, Straight Line
What is Distance?
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Distance can be defined as the amount of space that exists between any two points. It can also be further explained as the amount something has moved from one place to another.
- It is a scalar quantity and can be measured in units such as meters (m), kilometres (km), miles (mi), and so on.
- Distance is an important parameter in physics since it helps to calculate different physical quantities such as speed, velocity, and acceleration.
- Distance can be calculated by determining the length of the path covered by an object when it moves from one point to another.
Moreover, the change in position is proportional to the distance that an object travels. The distance measurement of distance usually takes place in units such as miles, kilometres, meters, centimetres, millimetres, yards, and inches.
Also Check: Frames of Reference
What is Time?
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Time is the progression of events. This process takes place in time, from the past to the present, and into the future. Time is something that can not be touched or tasted. One can only measure the passage of time. Time refers to the duration in hours, minutes, or seconds.
- Time, in physics, is a fundamental concept and it can be further expressed as the duration between two events or two points in time.
- It is often measured in units such as seconds, minutes, and hours.
- Time is relative, meaning that it can vary depending on the observer's position and velocity.
| Speed, Time and Distance Conversions
And,
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What is Speed?
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Speed is a scalar quantity as it defines only the magnitude and not the directions of the object in motion. A higher speed indicates that a given distance has been covered in a shorter time, or a longer distance covered in a given time. When it is said that a car is travelling at 50 kilometres per hour, it means that it will travel 50 kilometres in one hour.
| “Speed of any object refers to the magnitude of velocity.” |
A car, on the other hand, rarely travels at a consistent speed for an hour. In reality, it begins slowly before picking up speed. So, when we say a car travels at 50 km/h, we usually mean the whole distance it covers in an hour. It doesn’t matter if the car was travelling at a consistent speed during that hour or not. The speed calculated in this case is the vehicle's average speed.
- Average speed: The average speed is defined as the total distance covered by an object in a particular interval of time.
- Relative speed: The concept of relative speed is used when two or more bodies are moving with some speeds are considered, one body can be considered stationary and obtain the speed of the other body considering the stationary body, which is the sum total of the speeds if the bodies are moving in the opposite direction and the difference if they are moving in the same direction. Thus, this speed of the moving body with respect to the stationary body is referred to as relative Speed.
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Also Read:
| Concepts Related to Speed, Distance and Time | ||
|---|---|---|
| Relative Speed | Unit of Speed | Displacement Formula with Examples |
| Drift Velocity | Difference between Speed and Velocity | Equation of Motion |
| System of Units | Unit of Time | Velocity Definition |
Speed Distance Time Formula
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There is a direct relationship between the three basic variables of speed, distance and time. The formula of speed distance and time explains the relationship between these three variables.
Speed is directly related to distance and time. This is because the speed of an object refers to the distance travelled divided by time and is expressed as :
Speed = Distance/Time
⇒ s = d/t
Furthermore, one can also explain the relationship of time with the other two variables using this formula.
Time = Distance/Speed
⇒ t = d/s
And,
Distance = Speed × Time
⇒ d = st
The units used are:
- s = speed (meters/seconds, m/s)
- d = distance which is traveled (kilometres/meters, km/m)
- t = time (seconds, sec)
Solved Example of Speed, Distance and Time FormulaQues. A woman passes through a 600 m long street within 5 minutes. Determine her speed in km per hour. (1 mark) Ans. Distance = 600 m Time covered = 5 mins Therefore, Speed = Distance/Time Such that, Speed = \({{600} \over 5 \times60}\) m/sec = 2 m/sec Thus, \(2\times {{18} \over 5}\) km/hr = 7.2 km/hr |
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Relationship Between Speed, Time and Distance
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The relationship between speed, distance, time formula can be expressed mathematically as:
- Speed = Distance/Time: This is a mathematical formula which helps to define the relationship between speed, distance, and time. It states that the speed of an object is equal to the distance travelled divided by the time taken to cover that distance.
- Distance = Speed x Time: This formula helps to calculate the distance travelled by an object, given its speed and the amount of time it has travelled. It is based on the fact that speed is defined as the distance travelled by an object per unit of time.
- Time = Distance/Speed: With the speed increasing, the time taken is going to decrease and vice versa.
Applications of Speed, Time and Distance
Average Speed
Average Speed = (Total distance traveled)/(Total time taken)
- Case 1: For Constant Distance, Average speed = 2xy/x + y; here, x and y are the two speeds for which the same distance is covered.
- Case 2 – For Constant Time, Average speed = (x + y)/2; here, x and y are the two speeds at which we travelled for the same time.
Inverse Proportionality of Speed and Time
When the distance is constant, the speed is inversely proportional to Time.
S is known to be inversely proportional to 1/T while D being constant. Assuming that Speeds are in the ratio m : n, then the Time taken is going to be in the ratio n : m.
Thus, two methods are used to solve these questions:
- Using Inverse Proportionality
- Using Constant Product Rule
Previous Year Questions
- In vertical circular motion, the ratio of kinetic energy of a particle … [MHT CET 2016]
- A mass of 0.5kg moving with a speed of 1.5m/s … [VITEEE 2019]
- Speeds of 20m/s and 15m/s relative to the ground … [BITSAT 2019]
- An object is thrown vertically upward with a speed of 30m/s … [TS EAMCET 2017]
- An automobile travelling at 50 km/h … [JCECE 2005]
- A rifle shoots a bullet with a muzzle velocity of … [JCECE 2005]
- A body of mass 2kg has an initial velocity of 3m/s … [BHU UET]
- A particle starting from rest, moves in a circle of radius 'r' … [NEET 2019]
- In the given figure, a = 15 m/s2 … [NEET 2016]
- A ball is dropped from a high-rise platform at … [NEET 2010]
- A ball is thrown vertically downward with a velocity of 20m/s … [NEET 2020]
- A ball is thrown vertically upward … [NEET 2005]
- The displacement x of a particle varies with time t … [NEET 2005]
- A body is moving with velocity … [NEET 2011]
Things to Remember
- Speed is a scalar quantity as it defines only the magnitude and not the directions of the object in motion.
- Time is the progression of events. This process takes place in time, from the past to the present, and into the future.
- Distance can be defined as the amount of space that exists between any two points.
- Formula of speed: Speed = distance/time
- Formula of distance: Distance = speed × time
- Formula of time: Time = distance/speed
- Speed can be of two types: Relative Speed and Average Speed.
Sample Questions
Ques. The distance between two stations is 240km. A train takes 4 hours to cover this distance. Calculate the speed of the train. (2 marks)
Ans. Given,
Distance = 240km
Time = 4 hours
Using the speed distance time formula,
Speed = distance/time
Speed = 240/4 = 60km/h
Thus, the speed of the train would be 60km/h
Ques. Lilly is driving a scooter with a speed of 6 km/hr for 2hr. How much distance will she travel? (2 marks)
Ans. Given,
Speed of the scooter x = 6 km/hr
Time taken t = 2 hr
Distance traveled d = ?
Speed distance time formula is given as x =d/t
Distance traveled d = x × t
d = 6 km/hr × 2 hr
d = 12 km
Therefore, the distance travelled by Lily is 12km.
Ques. A Car Person Travels a Car at a Speed of 50 km Per Hour, How Far Can He Cover in 2.5 Hours? (2 marks)
Ans. Given,
Speed x = 50km/h
Time t = 2.5hours
Speed distance time formula is given as x =d/t
Substituting the values, we get
Distance = 50/2.5 = 125km
Hence, the car can travel 125 km in 2.5 hours.
Ques. 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? (2 marks)
Ans. Given,
Speed = 40miles/hour
Distance = 160 miles
Speed distance time formula is given as Time = Distance/speed
Time = 160/40 = 4
Thus, the time taken is 4 hours.
Ques. A man performs 3/5 of the total journey by rail, 17/20 by bus and the remaining 6.5 km on foot. His total journey is? (3 marks)
Ans. Let the total distance be x
According to the question,
3x/5 +7x/20 +6.5 = x
19x/20 +6.5 = x
x-19x/20 = 6.5
x/20 = 6.5
x = 6.5×20 = 130km
Ques. A golf cart is driven at its top speed of 27.0 km/h for a period of 10.0 minutes. Find out how far the golf cart travels? (3 marks)
Ans. Speed s = 27km/h
S = 27km/h × 1000m/1km × 1h/60min × 1min/60sec
s = 7.5 m/s
t = 10 min
t = 10min × 60s/1 min
t = 600 s
Finding the distance by using the formula:
d = st
d = (7.5 m/s) (600 s)
d = 4500 m
Therefore, the distance which the golf cart traveled is 4500 m, which is definitely equal to 4.5km
Ques. 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. (3 marks)
Ans. When boys run in the same direction,
Relative speed = ( 7 - 5) km/ hr = 2 km/ hr.
Time taken by boys = 20 minutes = 20/60h = 0.33 hour
Distance covered = Speed × Time
D = 2 × 0.33
D = 0.66km
Thus, The distance would be 0.66km
Ques. A train travels in a straight line at a constant speed of 60 km/h for a particular distance d and then travels another distance equal to 2d in the same direction at a constant speed of 80 km/h in the same direction as it was previously going. a) What is the average speed of the train during the whole journey? (2 marks)
Ans. The time taken t1 to cover distance d at a speed of 60 km/h is given by t1 = d / 60
The time t2 to cover distance 2d at a speed of 80 km/h is given by t2 = 2d / 80
Average Speed = distance/time = (d + 2d) / (d/60) + (2d/80) = 3d / (80d + 2d×60)/ (60×80)
= 3 d/(200d/4800) = 3d (4800)/200d = 72 km/h
Thus, the average speed of the train during the whole journey was 72km/h.
Ques. Anita and Anjali travel from Delhi to Jaipur in their respective cars. While Anita drives at 60 kmph, Anjali drives at 90 kmph. Thus, determine the Time taken by Anjali to reach Jaipur if Anita takes 9 hrs. (2 marks)
Ans. Since the covered Distance is constant in either of the cases, the Time taken is going to be inversely proportional to the Speed.
Here, the Speed of Anita and Anjali is in a ratio 60: 90 or simply, 2:3.
Thus, the ratio of the Time taken by Anita to that of Anjali is 3:2.
This means that if Anita takes 9 hrs, Anjali will take 6 hrs.
Ques. A person travels from A to B at a speed of 20 kmph. He, then, returns back at A at a speed of 30 kmph. Thus, determine his average speed. (2 marks)
Ans. Let the distance from A and B be 'd'
Thus,
Average Speed = total distance / total time
= (2d) / [(d/20) + (d/30)]
= (2d) / [5d/60)
= 24 kmph
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