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Question

The person driving a train is traveling at 30m/s applies the brake when he passes an amber signal. The Next Signal is 1.5 KM Down to the track and the train reaches it 75sec. later assuming a uniform acceleration, Find the constatnt velocity of the train at the second signal??

Answer 1

The most beautiful dynamics question i have ever handled.

very rough calculation suggests that time lost (25 s) [ if continued with 30m/s >t=50s] and uniform acceleration RIDER rips thro calculations.

can it be 11.25 m/s at the next signal.?

i am still working because extra time will decide the depth of triangles on V_T graph  

Answer 2

10 m/s is the answer.

Answer 3

average velocity can be defined in two ways.

first the train traveled 1500 meters in 75secs or 1500/75 m/sec.

second since the acceleration is constant the average speed = the initial velocity plus the final velocity all divided by 2, (Vi + Vf)/2 where Vi is said to be 30 m/s.

since the train can only have one average speed, these two equations equal each other.

1500/75 = (30 + Vf)/2

you can do the algebra to solve for Vf, which is the answer to the question

Answer 4

Using the v-t graph,

initial velocity, u = 30 m/s

final velocity, v =???

time, t = 75s

distance, s = 1500 m

Area of trapezium = 1/2 (v + 30) 75

1500 = 1/2 (v + 30) 75  

v = 10 m/s (ans)