SPEED,TIME & DISTANCE
Speed –
The speed of any object is defined by the said distance is covered by the said object in unit time.
Distance
Speed = ---------------,
Time
Distance = Speed X Time,
Distance
Time = --------------,
Speed
This is to be remembered that, when the distance is measured in kilometers (Km), the unit of time is the hour (h) and when the distance is measured in meters (m), the unit of time is considered by the second (s).
For your better understanding, there are some example are given below –
1) If a train covers 50 km in 30 minutes, as per the formula or rules the speed of the said train would be,
In 30 minutes the train covers 50km
50km
1 minute will be covered = -----------
30m
Now, in 1 hour = 60 minutes, the distance will be covered = 50 km X 60 m = ------------------
30 m
= 100 km/h 2) If a cycler covers a distance of 900 m in 4 minutes, then the speed of the cycler would be –
in 4 minutes = 4 X 60 seconds = 240 seconds covers 900 meters
900 m
In, 1 second will be covered = -----------
240 s
Now, in 1 hours = 60 minutes X 60 seconds = 3600 seconds, distance will
900 m X 3600 s
be covered = --------------------
240 s
= 13500 m/h = 13.5 km/h ( 1000 m = 1 km )
There are some unit of distance, speed, & time are given below –
Distance Time Speed
Kilometers (Km) Hours (h) Kilometers per hour (Km/h)
Meters (m) Minutes (m) Meters per Minute (m/m)
Centimeters (cm) Seconds (s) Centimeters per seconds (cm/s)
Conversion of Units –
Convert given km/h into m/m & cm/s
Example.1) 5 km/h
Ans.) As we all know that, 1 km = 1000 m = 100000 cm, and 1 hour = 60 minutes = 3600 seconds
5 X 1000 5 X 50 250
5 km/h = ------------ = ------------ = --------- m/m ..........(1)
60 3 3
5 X 100000 5 X 250 1250
5 km/h = ------------- = ------------ = -------- cm/s ……………(2)
3600 9 9
Example.2) 10 km/h
Ans.) As we all know that, 1 km = 1000 m = 100000 cm, and 1 hour = 60 minutes = 3600 seconds.
10 X 1000 10 X 50 50
10 km/h = ------------ = ----------- = -------- m/m ……...….(1)
60 3 3
10 X 100000 10 X 250 2500
10 km/h = -------------- = ------------ = -------- cm/s ………(2)
3600 9 9
Example.3) 25 km/h
Ans.) As we all know that, 1 km = 1000 m = 100000 cm, and 1 hour = 60 minutes = 3600 seconds
25 X 1000 25 X 50 1250
25 km/h = ------------ = ----------- = -------- m/m ………………(1)
60 3 3
25 X 100000 25 X 250 6250
25 km/h = -------------- = ------------- = ------- cm/s ………… (2)
3600 9 9
Uniform Speed–
In the preceding example, we assumed that the man walks at exactly the same pace all the time. In other words, we assumed that he covers equal distances in equal intervals of time. When a person or a body does this, we say that he/she/it has uniform speed.
For better understanding, if a train covers a distance of 2km in 5 minutes, its speed will be uniform provided it covers 2 km in each subsequent minute Uniform Speed –
In the preceding example, we assumed that the man walks at exactly the same pace all the time. In other words, we assumed that he covers equal distances in equal intervals of time. When a person or a body does this, we say that he/she/it has uniform speed.
For better understanding, if a train covers a distance of 2km in 5 minutes, its speed will be uniform provided it covers 2 km in each subsequent minute.
Average Speed-
In reality, however, things and people mostly do not have uniform speed. They pick up speed and slow down during the course of their travel. So, we calculate the average speed by dividing the total distance covered by a body by the total time it takes to cover the distance.
Total distance covered
Average speed = -----------------------------
Total time taken
Some important point –
1) When a moving train crosses an electric pole ( or a point or a person who is stationary ), it covers a distance equal to its own length.
So, time taken to cross the pole = time taken to cover a distance equal to the length of the train
The length of the train
= ------------------------------
The speed of the train
2) When a moving train crosses a platform or a bridge, it covers a distance equal to the sum of its length and the length of the platform.
So, time taken to cross a platform =
The length of the train + the length of the platform
------------------------------------------------- The speed of the train
Relative speed –
Suppose a goods train and an express train travel at 45 km/h and 90 km/h respectively on parallel tracks in the same direction. Then the distance between them will increase by (90 – 45) km or 45 km per hour. This is their relative speed. If on the other hand, the two trains travel in opposite directions, the distance between them will decrease by (90 + 45) km, i.e., 135 km per hour, which is their relative speed.
Thus the relative speed of two moving bodies is the rate at which the distance between them increases or decreases.
1) For two bodies moving in the same direction -
Relative speed = difference of their speeds.
2) For two bodies moving in opposite directions-
Relative speed = sum of their speeds.