Estimate Instantaneous Velocity

(m) = metres
(s) = Seconds

(m) 0 1 4 9 16 25
(s) 0 1 2 3 4 5

Estimate instantenous velocity? Explain working

From the given data it is obvious that

x= t^2 where x the distance in meters and t the time in seconds.

The instantaneous velocity at any instant is given by
dx/dt = 2t .

It is found from δx / δt when δt tends to zero .


At time t = 3 second
dx/dt = 2t .= 2*3 = 6 m/s
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By analytical method

We take two times 2 and 4 so that the average is 3 second

the distance moved is 16- 4 = 12

Instantaneous velocity is nearly 12 / ( 4-2) = 6 m/s .

Here it gives the actual values since the change in distance is uniform .

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Between 2s and 4s you have moved from 4m to 16m.

So during a period of 2s (4-2 = 2), the distance covered = 16-4 = 12m

Instantenous velocity -= distance/time = 12/2 = 6m/s

by observing given data, a relation between time and distance travelled can be formulated,
x=t^2
dx/dt=2t
at t=3
v= 6 m/s