Question

A train travels a distance of 60 km at uniform speed. If the speed of the train was reduced by 10 kmh-1, the time taken to travel the 60km will increase by 1/2h. Find the speed of the train at the beginning.

Answer 1

Initial speed is 32 m/s

At uniform speed, acceleration is 0, (a = 0).

When speed reduced, (v - u) = 2.78 ms-¹, t = 1800 sec, s = 60 ,000 metres.

From first equation of motion:

`{ \boxed{ \bf{v = u + at}}} \\ { \tt{(v - u) = at}}`

substitute:

`{ \tt{2.78 = (a * 1800)}} \\ { \tt{acceleration = 0.0015 \: {ms}^( - 2) }}`

from second equation of motion:

`{ \boxed{ \bf{s = ut + (1)/(2) a {t}^(2) }}}`

substitute:

`{ \tt{60000 = 1800u + ( (1)/(2) * 0.0015 * {1800}^(2)) }} \\ { \tt{1800u = 57570}} \\ { \tt{u = 32 \: m {s}^( - 1) }}`