Question

Find the Laplace transform of $u(-2t-1)$ where u(t) is unit step function

• A. $\frac{-e^{-s/2}}{s}$
• B. $\frac{e^{-s/2}}{s}$
• C. $\frac{-e^{s/2}}{s}$
• D. $\frac{e^{s/2}}{s}$

Answer 1

The correct option is C $\frac{-e^{s/2}}{s}$

$u\left(t\right)\stackrel{L.T.}{⟶}\frac{1}{s}$

$u(t-1)\stackrel{L.T.}{⟶}\frac{e^{-s}}{s}$

$u(2t-1)\stackrel{L.T.}{⟶}\frac{1}{2}.\frac{e^{-s/2}}{s/2}$

$u(-2t-1)\stackrel{L.T}{⟶}-\frac{1}{2}.\frac{e^{s/2}}{s/2}=\frac{-e^{s/2}}{s}$