Time and Distance

Speed refers to the rate at which an object travels through space and time. Kilometres per hour (km/h) and m/s are two common units of speed measurement. In order to calculate the average speed of an object over a certain distance, one can divide the distance travelled by the time taken to complete the journey.

Different things such as boats, races, streams, and clocks are all relevant to the concepts of speed, time and distance. This article explains how speed, distance, and time all work together.

Time and Distance Formula

Here are the formulas for time, speed, and distance: 

• Distance = Speed x Time
• Speed = Distance / Time
• Time = Distance / Speed

Time, Distance, and Speed—Units of Measurement

There are a variety of ways to measure speed, distance, and time.

• Minutes, hours, and seconds are all units of time. 
• Miles, kilometres, feet, and inches are units of distance. 
• Kilometres per hour or miles per second are units of speed.

Speed is measured in kilometres per hour (km/h) if the distance is measured in kilometres, and the time is measured in hours (hr). Let’s look at the conversions for speed, time, and distance.

For example, if a vehicle is travelling at 90 km/hr, then the speed in m/s will be 90 x 5/18 = 25 metres/second.

To convert from m/s to km/hr, we multiply the speed by 18/5. 

For example, if a vehicle is travelling at 20 metres per second, its speed in km/hr will be 20 x 18/5 = 72 km/hr.

Application of speed, time and distance

Let us delve into some common questions you are likely to see in competitive exams.

Average speed

• If a car drives 120 kilometres in 2 hours, then its speed will be distance/time = 120/2 = 60 km/hr. Despite the fact that the car’s average speed is 60 kilometres per hour, it is likely that its speed changed much during its journey. It may have reached speeds of up to 100 km/hr, reduced to 15 km/hr, or even come to a complete halt at a stoplight.
• When an item is moving at any given instant, its instantaneous speed is known as its velocity. What a car’s speedometer does is measure this type of data. In other words, the instantaneous speed is calculated by dividing the distance travelled in a short period of time by that short amount of time. The whole distance travelled divided by the total journey duration gives you the average speed.

Case Type 1: Constant Distance

Let us suppose that x and y are speeds at which a particular distance is covered. So, the  Average speed will be 2xy/x+y.

Case Type 2: Constant Time

Let us suppose that x and y are speeds at which distances have been travelled in the same amount of time. So, the average speed, in this case, will be (x+y)/2

Example:

Two people travelled from one place to another at 60 km/hr and 240 km/hr, respectively. The time taken collectively for them was 10 hours. Find the distance.

Solution:

The distance is the same for both of them. So, the time that they took will be inversely proportional to their speed. First, we find out the ratio of their speeds, which is 60:240 = 1:4

So, they will take 4:1 time to get there. The total time is 10 hours. So, one will take 2 hours to get there, while the other will take 8 hours. Therefore, the distance will be 240/2 = 120 km.

Meeting point 

Location P is the point at which two persons travelling in the same direction from points A and B meet. They will travel AB in total throughout the conference. Both of them will have the same amount of time to meet. Distances AP and BP will always be proportional to their respective speeds because time is a constant. If the distance between A and B is d, when two persons going from A and B meet for the first time, they walk a distance ‘d’ together. They will cover a ‘3d’ distance the second time they meet. Their third meeting covers a total distance of ‘5d’ between them, and so on.

Conclusion

To sum it up:

• If two moving bodies travel at a constant pace, the distance travelled will be precisely proportional to their duration of travel if they are both travelling at the same rate of velocity.
• When two moving bodies travel at the same speed for the same amount of time, the distance they cover is proportional to the time it takes them to get there.
• When two moving bodies are travelling at the same speed, their journey time is inversely proportional to the distance travelled.