I was coming back from my Driver's Education class, and something mathsy really stuck out to me.
One of the essential properties of a car is its current speed. Or speed at a current time. For example, at a given point in time in my drive, I could be traveling 40 mph. But what does that mean?
From my basic algebra classes, I've learned that speed = distance/time. So if I travel ten miles in half an hour, my average speed would be $20$ mph ($\frac{10 mi}{25 h}$).
But instantaneous velocity…you aren't measuring average speed for a given amount of time. You're measuring instantaneous speed over an…instantaneous amount of time.
That would be something like (miles) / (time), where time = $0$? Isn't that infinite?
And perhaps, in a difference of time = $0$, then I'd be travelling $0$ miles. So would I be said to be going $0$ mph at an instantaneous moment in time? I'd like to be able to tell that to any cops pull me over for "speeding"!
But then if miles = $0$ and time = $0$, then you have $\frac00$?
This is all rather confusing. What does it mean to be going $40$ mph at a given moment in time, exactly?
I've heard this explained using this strange art called "calculus" before, and it's all gone over my head. Can anyone explain this using terms I (a High School Algebra and Geometry and Driving student) will understand?
(I figured that my problem had numbers in it, and therefore has to do with Maths.)
Best Answer
I think there is a very clear meaning in the physical world: If, at some moment, you were going 40 mph, if you were to stop de/accelerating and just hold that velocity, you would cover 40 miles in 1 hour.