Speed: The speed of an object is the distance covered by it in unit time. We can write it as follows: $\displaystyle \text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Speed can be expressed in any of the following units… it could be Kilometers / Hour, Meters / Seconds, Feet / Seconds, Miles / Hours, etc.

Speed can be classified into two types:

Uniform Speed and Variable Speed: If the object covers equal distance in equal intervals of time, then it is said to be traveling with uniform speed. If not, its speed is said to be variable.

Average Speed: It is calculated by using the following formula: $\displaystyle \text{Average Speed }= \frac{\text{Total Distance Traveled}}{\text{Total Time Taken}}$

Relative Speed: The speed of one object with respect to the speed of another object is called relative speed.

Rules of finding the Relative Speed

1. If the two objects are moving in the same direction at a speed say $\displaystyle x$  km/hr and $\displaystyle y$  km/hr, then their relative speed $\displaystyle =(x-y)$  km/hr, where $\displaystyle x > y$
2. If two objects move in opposite directions at speeds of $\displaystyle x$  km/hr and $\displaystyle y$  km/hr respectively, then their relative speed is $\displaystyle = (x+y)$  km/hr

Problems on Trains

1. Time taken by a train $\displaystyle a$  meters long in passing a signal pole or a point or a man standing = Time taken by the train to cover $\displaystyle a$  meters
2. Time taken by a train $\displaystyle a$  meters long in passing an object $\displaystyle b$  meters long= Time taken by the train to cover $\displaystyle (a+b)$  meters
3. Time taken by a train $\displaystyle a$  meters long travelling at $\displaystyle x$  km/hr to pass a man travelling at $\displaystyle y$  km/hr in the same direction = Time taken by the train to cover a meters at $\displaystyle (x-y)$   km/hr.
4. Time taken by a train a meters long travelling at $\displaystyle x$  km/hr to pass a man travelling at $\displaystyle y$  km/hr in the opposite direction = Time taken by the train to cover a meters at $\displaystyle (x+y)$  km/hr.
5. Time taken by a faster train of length $\displaystyle a$  meters travelling at $\displaystyle x$  km/hr to over take a train of length b meters traveling at a speed of $\displaystyle y$  km/hr in the same direction = Time taken by the train to cover $\displaystyle (a+b)$   meters at $\displaystyle (x-y)$  km/hr.
6. Time taken by a faster train of length $\displaystyle a$  meters travelling at $\displaystyle x$  km/hr to over take a train of length b meters traveling at a speed of $\displaystyle y$  km/hr in the opposite direction = Time taken by the train to cover $\displaystyle (a+b)$   meters at $\displaystyle (x+y)$  km/hr.

Problems on Boats and Streams

1. If the speed of the boat is $\displaystyle x$  m/s in still water and the speed of the stream is $\displaystyle y$  m/s, then:
1. $\displaystyle \text{Speed of the boat downstream } =(x+y)$  m/s
2. $\displaystyle \text{Speed of boat upstream } =(x-y)$  m/s
2. If the speed of the boat down stream is $\displaystyle x$  m/s and upstream is $\displaystyle y$  m/s, then
1. $\displaystyle \text{Speed of the boat in still water } = \frac{x+y}{2}$  m/s
2. $\displaystyle \text{Speed of the stream } = \frac{x-y}{2}$   m/s