The speed of a train increases at a constant rate \[\alpha \] from zero to v, and then remains constant for an interval, and finally decreases to zero at a constant rate \[\beta \]. If L be the total distance travelled, then the total time taken is

• A. \[\frac{L}{v}+\frac{v}{2}\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)\]           
• B. \[\frac{L}{v}+\frac{2}{v}\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)\]
• C. \[\frac{L}{v}+2v\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)\]  
• D. \[\frac{L}{v}+\frac{1}{v}\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)\]