t(sec) 1 1.5 2 2.5

v(ft/sec) 12.2 1.3 13.4 13.7

velocity of an object moving along a line at various times.
How do I estimate the object's acceleration(in ft/sec^2) at t=1


t(sec) 1, 1.5, 2, 2.5
v(ft/sec) 12.2 ,1.3 ,13.4 ,13.7

The second velocity of 1.3ft/sec is an error, it has to be 13.?

Look at the last data: delta T= .5 sec
deltaV= .3ft/sec

acceleration estimate: deltaV/DeltaT

You can do more of these, then average.

Overall, delta T=1.5 sec delta V 1.5

Now at t=1. Using your data, which I find the V at 1.5 sec to be in error...

delta t=.5 delta V= -10.9 But I suspec the V is wrong data.

To estimate the object's acceleration at t=1, you can use the concept of average acceleration.

Average acceleration can be calculated by finding the change in velocity (delta V) and dividing it by the change in time (delta T).

Looking at the given data:
t(sec): 1, 1.5, 2, 2.5
v(ft/sec): 12.2, 1.3, 13.4, 13.7

To estimate the acceleration at t=1, we need to find the change in velocity and the corresponding change in time. However, there seems to be an error in the second velocity data point (1.3ft/sec), as it doesn't fit the trend and appears to be an outlier.

Assuming the second velocity value is incorrect, we can use the next two data points:

Delta V: 13.4 - 12.2 = 1.2 ft/sec
Delta T: 2 - 1.5 = 0.5 sec

Now we can estimate the average acceleration:
Acceleration = Delta V / Delta T = 1.2 ft/sec / 0.5 sec ≈ 2.4 ft/sec^2

Keep in mind that this is just an estimate based on the available data. If there are further inconsistencies or errors in the given data, it may affect the accuracy of the estimation.