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Mathematical Relationship Between Velocity & Time

It's a question we've all heard in school at one time or another: Two trains start traveling toward each other from different places on the same track at the same time. They are traveling at different speeds. When will they collide? The answer to this question requires understanding the mathematical relationship between time and velocity. This is a deceptively complex equation, involving variables of acceleration and distance.
  1. Significance

    • The velocity/time ratio is a fundamental aspect of kinematics, defined as the study of motion. This has practical applications in many areas of daily life. Professional auto racing teams, for example, must track speeds and distances to formulate strategy. NASA engineers utilize the time-velocity equation to determine launch windows for reaching orbit. Even an activity such as skydiving utilizes velocity and time calculations -- airplanes must fly high enough to allow enough time for parachutes to fully engage for a safe, controlled descent to the ground.

    Basic Relationship

    • The easiest way to understand velocity in relation to time is to examine an object moving at a perfectly constant speed. Consider a car moving at 60 mph. Given that there are 60 minutes in an hour, this means the car will travel one mile per minute. This can be expressed in the following equation: (R)ate multiplied by (T)ime equals distance, or R x T = D. In this example, the rate is 1 mile per minute, the time is 1 minute and therefore the distance is 1 mile.

    Advanced Concept

    • But, objects do not typically move at a constant speed, introducing the variable of acceleration. Consider once again our car traveling 60 mph. If only because of traffic, this car will have to speed up or slow down along the way. In this case, you'll have to calculate the rate of change in distance and time to find distance, expressed as R=Change in (D) distance divided by change in (T) time. So, if the car takes 20 minutes to travel 10 miles, its velocity is an average of 50 mph or 10 miles in 20 minutes. The car is traveling two miles per minute, or average speed of 30 mph.

    Average Speed

    • While average speed is a useful data point, it can be misleading. Obviously, our car is not traveling at 30 mph when it heads down the exit ramp to the highway or on an open road. It is possible using our data, however, to calculate the speed of the object at any particular point during its travels. This is called instantaneous speed. A good way to address instantaneous speed is to calculate average speed over a short distance of the car's travels.

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