The speed of train increases at a constant rate from zero to and then remains…

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

The speed of 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

. The total distance travelled by the train is

l

. The time taken to complete the journey is

t

. Then, (A)

t=\frac{l(\alpha+\beta)}{\alpha\beta}

(B)

t=\frac{l}{v}+\frac{v}{2}\left(\frac{1}{\alpha}+\frac{1}{\beta}\right)

(C)

t

is minimum when

v=\sqrt{\frac{2l\alpha\beta}{(\alpha-\beta)}}

(D)

t

is minimum when

v=\sqrt{\frac{2l\alpha\beta}{(\alpha+\beta)}}