Instantaneous speed without using calculus

[rajeshmarndi]

Say a particle cover y=t^2 distance.

at t=1s total distance cover = 1m
at t=2s total distance cover = 4m
at t=3s total distance cover = 9m
at t=4s total distance cover = 16m

So the instantaneous speed at t=2s is 9 - 4 = 5m i.e 5m/s.

To get the instantaneous speed at t=2s and t=3s, I take the instantaneous speed 5m/s at t=2s, as the average instantaneous speed between t=2s and t=3s as 5.

So the instantaneous speed at t=2s and t=3s become 4m and 6m. Also the instantaneous speed

at t=2.1s become 4.1
at t=2.3s become 4.3 and so on.

Here we get the instantaneous speed without using Δt→0. But I know to calculate instantaneous speed, calculus was invented.

Thanks.

[edit :]

at t=2.1s become 4.2
at t=2.3s become 4.6 and so on.

 

[phinds]

at t=2.1s become 4.1

wrong, it's 4.2

at t=2.3s become 4.3

wrong, it's 4.6

Here we get the instantaneous speed without using Δt→0.

And you get it incorrectly.

Was there as question in all of this or did you just want to demonstrate incorrect extrapolation?

 

[rajeshmarndi]

at t=2.1s become 4.1
at t=2.3s become 4.3 and so on.

correction ...
at t=2.1s become 4.2
at t=2.3s become 4.6 and so on.