Grade 11General Physics

Velocity of a train increases at a constant rate f1 from 0 to v and remains constant for an interval and finally decreases to 0at f2.
If x=total distance. Prove that the total time taken is x/v+v/2(1/f1+1/f2).

Nivashini Elango

8 Years agoGrade 11

1 Answer

Arun

8 Years ago

Let the train accelerate from the velocity 0 to v at this rate α in time t1 and distance is d1.

f1 = v-0/t1 = v/t1

t1 = v/ f1

then d 1= ½ * ( )^2

= v^2/ 2 f1

After that it moves with constant speed v in time t2

Then d2 = vt2

Then it decelerates from v to zero in time t3 with the rate f2

t3 = v/ f2

No w using

v²+ u² = 2 f2 d3
0+ v² = 2 f2 d3
d3 = v²/2 f2

Total distance (d) = v^2/ 2 α + vt2 + v²/2 f2

d= v^2/ 2 f1 + vt2 + v²/2 f2

t2 = d/v- v/ 2 v/2

Then Total time

T = + d/v- v/ 2 v/2 + v/

=d/v + v/2

As the total distance is 1

Then T = 1/v + v/2[1/f1 +1/f2].

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Velocity of a train increases at a constant rate f1 from 0 to v and remains constant for an interval and finally decreases to 0at f2.If x=total distance. Prove that the total time taken is x/v+v/2(1/f1+1/f2).

Nivashini Elango

1 Answer

Arun

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