Speed is a scalar quantity; that is, it can be described by a number only; for example 10 kilometers per hour. Velocity is described as a numerical value plus a direction. It is a vector quantitiy; meaning that it measures a total displacment of an object or person. If you were running and made a complete circuit; finishing from where you started, your velocity would be zero because you haven’t made any net gain in distance. Vector quantities, therefore have both a speed and a direction. You will increase your velocity as long as you keep moving in one direction. So that same runner, running the same distance in a straight line for 5 kilometers west at 10 kilometers per hour has travelled a total distance of .5 kilometers west.

In summary, speed is a numerical value only and velocity has a numerical value and a direction. Velocity = change in direction/change in time; whereas speed is the absolute value of distance/time. Absolute value means that if an object is moving forwards or backwards, it will not have a negative number in front of it. So if you travelled 30 kilometers per hour backwards from your current position, you would not describe your speed as -30 kilometes per hour; it would simply be 30 kilometers per hour.

An integer is a whole number. Fractions and decimals are not included in this set. They are sometimes also called natural numbers and consist of the numbers that you can count, starting at zero, and their negative counterparts for example 2, 6, -89; are all integers, while 2.4, 66.7 are not integers. To answer the question of what is the smallest integer, it is negative infinity; there is no smallest integer because there will always be one number lesser.