Cars Velocity as Slope

What’s the point?

In math the word “slope” is used for anything changing. It’s the same idea as slope in normal life, that is the change in height as you move forward, but generalized to anything that’s changing. For example, the distance a car moves vs the time it’s been moving is its velocity

 \mathbf{Slope}\ =\ \frac{\mathbf{Vertical}\ \mathbf{Change}}{\mathbf{Horizontal}\ \mathbf{Change}} 

TL;DW

  • The examples are for different kinds of cars’ velocity. The vertical axis is distance, so the Vertical Change is how far the car has moved in meters. The horizontal axis is time, so the Horizontal Change is the time the car has been moving in seconds.

    \mathbf{Velocity}\ =\ \frac{\mathbf{Distance}}{\mathbf{Time}\ }

  • The distance is in meters, the time is in seconds, so the distance divided by the time is meters per second, a velocity

    \mathbf{meters\ per\ second}\ =\ \frac{\mathbf{Meters}}{\mathbf{Seconds}\ }

  • The faster the car, the steeper the slope, which is to say: the greater the value of the slope. Not too surprising since the slope for these examples is velocity and faster cars have a greater velocity than slower cars. 😉

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