Question

The energy of a system as a function of time `t` is given as `E(t) = A^(2)exp(-alphat)`, `alpha = 0.2 s^(-1)`. The measurement of `A` has an error of `1.25%`. If the error In the measurement of time is `1.50%`, the percentage error in the value of `E(t)` at t = 5 s` is

Answer 1

Correct Answer - `4`
`E(t) = A^(2) e^(- alpha t)`
In `E = 2 In A - alpha t`
`:. (Delta E)/(E) xx 100 = 2 (Delta A)/( A) xx 100 - alpha t xx 100` (i)
For time : `(Delta t)/(t) xx 100 = 1.5`
At `t = 5 s, Delta t = ( 1.5 xx 5 )/( 100) = ( 7.5)/( 100)`
Using Eq(i)
% error in `E = 2 xx ( 1.25) + alpha xx ( 7.5)/(100) xx 100`
`= 2.5 + 1.5 = 4`