Kinematic Velocity As a Function of Distance

Kinematics is the branch of physics that studies the motion of objects and velocity is one of its basic concepts. In everyday life, velocity and speed are used interchangeably to describe, for example, how fast a car, a sprinter or a bullet moves, even though physicists have a distinct definition for each term. As velocity's formula includes the variable of displacement, you can form a function of two variables that gives you the distance covered on a set velocity and time value.
  1. Velocity Defined

    • In physics, speed is defined as an object's displacement divided by time interval. In other words, it's the distance traveled within a set period of time. Therefore, the speed of a car can be 60 miles per hour, for example. However, when you add the object's direction and say that the car runs at 60 miles per hour north, then you describe velocity.

    Displacement Vs. Distance

    • Displacement and distance are two terms that--just like velocity and speed--are used interchangeably in everyday life. In physics, displacement--denoted as "Δx"--refers to the length of the straight line that connects the object's initial and final positions, while distance is the length of the route that you followed to reach your destination. However, on the function of distance described below, distance has the same meaning with displacement. This happens because it's impossible to form a single function that applies for the unlimited number of routes that you can follow in reality.

    Velocity as a Function of Distance

    • Velocity equals v = Δx / Δt and is measured in miles per second, or any other measurement of length and time. Therefore, distance equals to Δx = v × Δt. Time interval isn't a constant, as a car can run for 30 seconds or 30 minutes, for example, and you must form a function of two variables with velocity being the "A" variable and time interval the "B" variable. Therefore, you have the function f(A,B) = A mi/h × B h.

    Example of the Function

    • Suppose you have a car with a velocity of 140 miles per hour east, which runs for 5 hours. Using the function, you get f(A,B) = 140 mi/h × 5 h = 700 mi × h/h. Erase the h/h from your measurement unit's fraction to get the distance traveled, which is 700 miles. You can also ignore the units of measurement throughout the process and just add the unit of length--"miles" in this example--to the function's result.

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