A ball moves along a 1D coordinate system with the following motion parameters a

Question

A ball moves along a 1D coordinate system with the following motion parameters at time t = 0 s: x0 = 5.5 m and v0 = 3.3 m/s. The ball has a constant acceleration of 2.5 m/s2 during the entire motion which occurs over a time of 2.6 s. Assume that an error in position of 9 % is acceptable in this application over the entire motion. How many rows N will be needed in the table to model the entire motion to within the required error even though you are leaving out the final term of 1/2 a (At t)2 ) present in the exact position expression?

Explanation / Answer

Solution :-

Given, time (t) = 0 sec

x0 = 5.5 m and v0 = 3.3 m/s and a = 2.5 m/s^2

Time (t' ) = 2.6 s

We know, S = ut+1/2at^2

= 3.3(2.6)+1/2(2.5)(2.6)

= 11.83 m

The error in the position is given by,

9×5.5/100 = 0.495 m

so, error in position = 5.5-0.495 = 5.005

So, number of rows = 2× 11.83/5.005 = 4.72 (for entire motion)

That is, five rows are needed to model the entire motion.

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