anonymous
  • anonymous
The velocity of a train increases at a constant rate of A from velocity 0 to v and then remains constant for some time and then finally decreases to 0 at a constant rate of B. If the total distance covered by the train is x then show that the total time taken is t = (x/v) + (v/2)[(1/A)+(1/B)]
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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missMob
  • missMob
hmm
kropot72
  • kropot72
Time taken for train to accelerate = v/A .............(1) Time taken for train to decelerate = v/B ............(2) Distance travelled during acceleration = average speed * time = (v/2) * (v/A) = \[\frac{v ^{2}}{2A}\ ..........(3)\] Distance travelled during deceleration = average speed * time = (v/2) * (v/B) = \[\frac{v ^{2}}{2B}\ ..........(4)\] Distance travelled at constant speed v is given by \[x-(\frac{v ^{2}}{2A}+\frac{v ^{2}}{2B})=x-\frac{v ^{2}}{2}(\frac{1}{A}+\frac{1}{B})\ .....(5)\] The time travelled at constant speed v is found by dividing the distance given by equation (5) by the speed v, giving the following result \[\frac{x}{v}-\frac{v}{2}(\frac{1}{A}+\frac{1}{B})\ ...............(6)\] The total time taken is found by adding the times in (1) and (2) to the time in (6) as follows: \[Total\ time=\frac{x}{v}-\frac{v}{2}(\frac{1}{A}+\frac{1}{B})+\frac{v}{A}+\frac{v}{B}=\frac{x}{2}+\frac{v}{2}(\frac{1}{A}+\frac{1}{B})\]

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