# 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.$$A \ m/sec = A \times \frac{18}{5} \ km/hr$$