The displacement and velocity values at time, t = 8 seconds are; 11.76 and -0.545 respectively
How can interpolating be used to find variable values at a given time?
Part A
The possible values in the table are;
Displacement;
t = 7 seconds, y = 10.02
t = 8 seconds, y = 11.01
t = 9 seconds, y = 13.5
Velocity;
t = 7 seconds, y = 0.06
t = 8 seconds, y = -0.05
t = 9 seconds, y = -1.15
The equation for interpretation which is a form of linear equation is presented as follows;
[tex]y - y_0 = \frac{y_1 - y_0}{x_1 -x_0} \times (x - x_0)[/tex]
Interpolating for the displacement at t = 8.0 seconds is as follows;
[tex]y - 10.02 = \frac{13.5 - 10.02}{9 - 7} \times (8 - 7)[/tex]
Which gives the displacement at t = 8.0 seconds as 11.76
Interpolating for the velocity at t = 8.0 seconds is as follows;
[tex]y - 0.06 = \frac{(-1.15) - 0.06}{9 - 7} \times (8 - 7)[/tex]
Which gives the velocity at t = 8.0 seconds as -0.545
The values for the displacement and velocity obtained by interpolation (11.76 and -0.545) are different from the displacement and velocity values in the table at t = 8 which are; 11.01 and -0.05 respectively
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