Question

A ball moves along a 1D coordinate system with the following motion parameters at time t = 0 s: x0 = 9.5 m and v0 = 0 m/s. The ball has a constant acceleration of 2.6 m/s2 during the entire motion which occurs over a time of 1.8 s. Assume that an error in position of 7 % 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 ( Δ t )2 ) present in the exact position expression?

Answer 1

given

x_o = 9.5 m

t = 0 sec

v_o = 0 m/sec

a = 2.6 m/sec²

dt = 1.8 sec

an error in position of 7 % is acceptable

using kinematic equation

s = v_o t + 1/2 a dt²

= 0 x 1.8 + ( 0.5 x 2.6 x 1.8² )

s = 4.212 m

7 % position of particle

7 x 9.5 / 100 = 0.665 m

error in the position is = 9.5 - 0.665

= 8.835

so no of rows = 2 x 4.212 / 8.835

finally the no of rows are equal to 0.9534