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Instantaneous Velocity

Teacher/Instructor Matt Jones
Matt Jones

M.Ed., George Washington University
Dept. chair at a high school

Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids.

Instantaneous velocity is the velocity of an object in motion at a specific point in time. This is determined similarly to average velocity, but we narrow the period of time so that it approaches zero. If an object has a standard velocity over a period of time, its average and instantaneous velocities may be the same. The formula for instantaneous velocity is the limit as t approaches zero of the change in d over the change in t.

Let's talk about instantaneous velocity. Instantaneous velocity is the change in distance over the change in time. You may recognize it as 100 kilometers an hour it's what you see on your odometer or your speedometer when you're driving okay? Example let's say I get in my car and I set the cruise control for 50 kilometers an hour and I drive for an hour, well my instantaneous velocity that whole time using my cruise control is 50 kilometers an hour okay? Again since we said in velocities we also have to give the direction so I was driving 50 kilometers an hour east okay? Alright now let's say I get my in car and do that same drive but there's a lot of traffic and I'm trying to accelerate past cars and I'm turning past cars and I'm braking because I can't get around a car. I still travel that hour in 50 kilometers east so my average velocity is still 50 kilometers an hour east okay? But my instantaneous velocity was always changing when I was accelerating, when I was braking even when I was turning the car because remember velocity direction counts so when I change direction of the car that changed the velocity okay?

Well why is instantaneous velocity so difficult to calculate? Well it's the change in distance over the change in time but we want that time to be as short in interval as possible it's like a snapshot of what your of what your speed was at that one particular second, half second, thousandth of a second right? So to get that change in time to equal 0 we need to use a calculae Calculus formula and it gets a little bit complicated but that's how we calculate instantaneous velocity.