How do you find instantaneous speed?

[navneet]

how can I find the instantaneous speed when t=6 seconds for the following, and would it be any differnt if i draw a graph and find it using with the line of best fit.

d (m) l t (s)
---------------------------
0 l 0
2 l 1.59
4 l 2.37
6 l 3.87
8 l 3.98
10 l 6.09
12 l 8.90
14 l 8.66
16 l 9.23
18 l 10.18

 

[mathman]

Your approach is probably the most reasonable. There are formulas one could use, but they would effectively get the same result as you could by a good curve fit. The formulas are curve fitting themselves.

 

[quicknote]

Instantaneous speed is the rate at which an object is moving at a specific moment in time. To find the instantaneous speed at t=6 seconds, you can use the formula v=Δd/Δt, where Δd is the change in distance and Δt is the change in time. In this case, the change in distance is 6 meters (d=6) and the change in time is 3.87 seconds (t=3.87). Therefore, the instantaneous speed at t=6 seconds is 6/3.87=1.55 m/s.

If you were to plot this data on a graph and find the line of best fit, you can also find the instantaneous speed at t=6 seconds by finding the slope of the line at that point. The slope of a straight line is equal to the instantaneous speed at any point, so the result would be the same.

However, it is important to note that the line of best fit may not always be a straight line and may not accurately represent the instantaneous speed at a specific moment in time. It is always best to use the formula v=Δd/Δt to calculate instantaneous speed.