Time, Speed and Distance: Introduction


Speed: Distance covered by a moving object in per unit time interval is known as speed.$$ Speed = \frac{Distance \ Covered}{Time \ Taken} $$

Note (1): When time is constant, then speed is directly proportional to distance.$$ Speed \propto Distance $$

Note (2): When speed is constant, then time is directly proportional to distance.$$ time \propto Distance $$

Note (3): When distance is constant, then speed is inversely proportional to time.$$ speed \propto \frac{1}{time} $$

Example (1): A person traveles \(10 \ km\) in \(2\) hours, what could be the speed of the person?

Solution: Given values, Distance = \(10 \ km\), Time taken = \(2 \ hr\), then $$ Speed = \frac{Distance \ Covered}{Time \ Taken} $$ $$ Speed = \frac{10}{2} = 5 \ km/hr $$

Example (2): A person traveles at the speed of \(30 \ km/hr\) and completed his journey in \(2\) hours, the find out the distance covered by the man?

Solution: Given values, speed = \(30 \ km/hr\), Time taken = \(2 \ hr\), then $$ Speed = \frac{Distance \ Covered}{Time \ Taken} $$ $$ 30 = \frac{Distance \ covered}{2} $$ $$ Distance \ covered = 60 \ km $$

Relative Speed:

Case (1): If two objects are moving in the same direction at the speed of \(s_1\) km/hr, and \(s_2\) km/hr, respectively. then, $$ Relative \ Speed = \left[s_1 - s_2\right] $$

Example (1): A bus is moving at the speed of \(60 \ km/hr\), and a car is moving \(50 \ km/hr\) on the same road and in the same direction then, what could be the relative speed of bus and car?

Solution: Given values, speed of bus \(s_1 = 60 \ km/hr\), and speed of car \(s_2 = 50 \ km/hr\) then$$ Relative \ Speed = \left[s_1 - s_2\right] $$ $$ = \left[60 - 50\right] = 10 \ km/hr $$

Example (2): If two trains moving in the same direction with the relative speed of \(20 \ km/hr\) and the speed of first train is \(40 \ km/hr\), then find the speed of second train?

Solution: Given values, relative speed \(= 20 \ km/hr\), and speed of first train \(s_1 = 40 \ km/hr\) then$$ Relative \ Speed = \left[s_1 - s_2\right] $$ $$ 20 = \left[40 - s_2\right] $$ $$ s_2 = 20 \ km/hr $$

Case (2): If two objects are moving in the opposite direction at the speed of \(s_1\) km/hr, and \(s_2\) km/hr, respectively. then $$ Relative \ Speed = \left[s_1 + s_2\right] $$

Example (1): A bus is moving at the speed of 60 km/hr, and a car is moving at the speed of 50 km/hr on the same road and in the opposite direction then, what could be the relative speed of bus and car?

Solution: Given values, speed of bus \(s_1 = 60 \ km/hr\), and speed of car \(s_2 = 50 \ km/hr\) then$$ Relative \ Speed = \left[s_1 + s_2\right] $$ $$ = \left[60 + 50\right] = 110 \ km/hr $$

Example (2): If two trains moving in the opposite direction with the relative speed of \(75 \ km/hr\) and the speed of first train is \(45 \ km/hr\), then find the speed of second train?

Solution: Given values, relative speed \(= 75 \ km/hr\), and speed of first train \(s_1 = 45 \ km/hr\) then$$ Relative \ Speed = \left[s_1 + s_2\right] $$ $$ 75 = \left[45 + s_2\right] $$ $$ s_2 = 30 \ km/hr $$

Unit Conversions:

(1). Conversion of km/hr to m/sec. $$ A \ km/hr = A \times \frac{5}{18} \ m/sec $$

(2). Conversion of m/sec to km/hr.$$ A \ m/sec = A \times \frac{18}{5} \ km/hr $$