Why speed was defined as distance over time ? Are there possible ways to define speed like distance plus time or distance minus time or distance times time
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$\begingroup$ What properties do we want when we define speed? $\endgroup$– AnujCommented Feb 24, 2019 at 11:07
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$\begingroup$ You can't just add quantities that have different units. What would the result even mean if you add a distance of $x$ metres to a time of $t$ seconds? $\endgroup$– PM 2RingCommented Feb 24, 2019 at 11:07
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1$\begingroup$ OTOH, you can do stuff like $w=\ln\left(\frac{ct+x}{ct-x}\right)/2$, and that turns out to be more useful than speed when you get close to the speed of light. $\endgroup$– PM 2RingCommented Feb 24, 2019 at 11:13
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1$\begingroup$ I agree that we can't add or subtract quantities which have different units but we can multiply them so why don't we define speed as distance times time $\endgroup$– AnujCommented Feb 24, 2019 at 11:15
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2$\begingroup$ Concepts like "speed", "distance" and "time" mean something in the real world we live in. If you want to invent a new concept like "flurp" which equals distance $\times$ time, that's fine - except that in the real world there isn't any obvious use for "flurp", which is why it doesn't already have a name. $\endgroup$– alephzeroCommented Feb 24, 2019 at 12:02
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If you think about what we mean when we say velocity, it is how much the position changes over some period of time. This is clearly given by $v=s/t$. Move double the distance in the same time, you have double the speed. Or the same distance in half the time, also double the speed.
Distance plus or minus time makes no sense, as the units don't match. Distance times time also does not have the properties we want if we ask how quickly something going from $A$ to $B$, and has no significance in physics that I'm aware of.
