Speed, Time & Distance

Speed of an object is defined as the distance covered by it in unit time.

 To convert speed from km/h to m/s, multiply by

 To convert speed from m/s to km/h, multiply by

Average Speed

Generally, a vehicle does not covers the entire distance at a uniform speed. In such a case, the average speed is calculated by

 In travelling equal distance with speeds x and y, the average speed is expressed as

Relative Speed

The relative speed of a moving body with speed x km/h in relation to another body moving with speed y km/h

• in same direction is difference of their speed i.e., (x – y) km/h, where x > y
• in opposite direction is the sum of their speeds i.e., (x + y) km/h

If a body travels at a speed of x km/h, it reaches the destination late by t₁ min but if the same body travels at a speed of y km/h, then it reaches the destination t₂ min earlier, then the distance is

Example:
If Aman cycles at 10 km/h, he reaches the office late by 4 minutes; if he cycles at 12 km/h, he reaches the office early by 2 minutes. Find the distance of the office from his home.

Solution

Relative Speed & Motion of Trains

• If two trains of length x km and y km are moving in opposite directions at the speeds of u km/h and v km/h, then time taken by the trains to cross each other
  
• If two trains of length x km and y km are moving in the same direction at the speeds of u km/h and v km/h, where u > v, then time taken by faster train to cross the slower train
  
• Time taken by a train x metres long in passing a single post or a pole or a standing man = Time taken by the train to cover x metres.
• Time taken by a train x metres long in passing a stationary object, for example a bridge or a tunnel, of length y metres = Time taken
  by the train to cover (x + y) metres.
• If two trains A and B start at the same time from two points P and Q towards each other and after crossing they take a and b hours in reaching Q and P, respectively. Then, A speed : B speed =

Example:
A train travelling at 90 km/h passes through a tunnel 675 m long. Find how long a passenger travelling by the train remains inside the tunnel.

Solution Speed of the train

The passenger remains inside the tunnel till the train covers the distance equal to the length of the tunnel i.e., 675 m

Therefore, the time for which the passenger remains inside the tunnel

Example:
Two trains of equal lengths are running on parallel lines in the same direction at the rate of 60 km/h and 40 km/h. The faster train passes the slower train in 45 secs. The length of each train is?

Solution

Boats and Stream

The direction along the stream (water current) is called downstream and the direction against the stream is called upstream.

• If the speed of a boat in still water is x km/h and the speed of the stream is y km/h, then
  1. Downstream speed = (x + y) km/h
  2. Upstream speed = (x – y) km/h
• If the downstream speed is u km/h and upstream speed is v km/h, then
  Speed of boat in still water
  
  Speed of stream
  

Example:
A man can row 20 km/h in still water. If it takes him thrice as long to row up as to row down the river. Find the speed of the stream.

Solution Ratio of time taken upward and downward = 3:1

Hence, ratio of upward and downward speed = 1:3

Let man’s upstream speed (v) be x km/h

Then his downstream speed (u) will be 3x km/h

Speed in still water

Given, 2x = 20 ⇒ x = 10 km/h

∴ Downstream speed (u) = 3x = 30 km/h
And, Speed of stream

Practice Questions on Speed, Time & Distance