Q1.

A train passes a station A at 40km/hr and maintains this speed for 7km and is then uniformly retarded, stopping at B, which is 8.5km from A. A second train starts from A at the instant the first train passes and being accelerated for part of the journey and uniformly retarded for the rest stops at B at the same time as the first train. What is the greatest speed of the second train?

Q2.

Two trains each having a speed of 30km/hr are headed at each other on the same straight track. A bird that can fly at 60km/hr flies off one train when they are 60km apart and heads directly for the other train. On reaching the other train it flies directly back to the first and so forth. Find :                                                     

a) how many trips can the bird make from one train to the other before the train collide?                                            

b) What is the total distance travelled by the bird?

EDITED............the answer to first is 68km/hr

PLEASE CHECK THE DETAILED SOLUTION IN BELOW POST.............

is ans to 1st ques is 55.54 km/hr

No ans to the first ques. is 68km/hr.

Now try again and also tell me the method.

No ans to the first ques. is 68km/hr.

Now try again and also tell me the method.

first calculate the total distance traveled and time taken by the train A

TOTAL DISTANCE TRAVELED BY TRAIN A= 8.5KM

total time taken= 7/40hrs + time taken to retard and stop

so to find time taken to retard and stop

first find the retardation i.e v^2 = u^2+2as here v=0 as it stops at end

so a= - (40*40)/(2*1.5)

so for time use v=u + at where v=0

so t = 3/40hrs



SO THE TOATL TIME TAKEN BY FIRST TRAIN = 7/40 + 3/40 HRs= 1/4HRS



AS GIVEN TIME TAKEN BY TRAIN B is same as A and also the distance travelled is also same ....................so train b will accelerate for half time(1/8 hrs) and half distance(8.5/2km)

v^2 = 2 * a * 8.5/2

v= a* 0.125

so v^2  = (v*8.5)/.125

v= 68km/hr

@sahil

thanks ur ans is correct now try the second one.

@sahil

thanks ur ans is correct now try the second one.

relative speed=60km/hr

time takem to cover 60km by two trains is 60/60= i hr

since speed of bird is 60 km/hr therefore distance covered bysuppose the   bird in 1 hr is 60 km ans to 1st part.

consider vel of 1 train to be 60 and other to be zero and suppose it is at distance x from fly

so let the come to the moving trainin time t

d of trian 60 t and d of bird also 60t adding both =120t

so t=sum of both(x)/120t and so dist of bird =60/120*x=x/2and in2nd 3 rd and thus n trips distance of car from fly would be (1/2)raise to power n-1 so trips would be infinite

@molu

your answer to  both the parts of Q 2 are correct but i m not able to understand the sol to part 1 which u had done later.please explain again.