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A particle is moving with a uniform acceleration along a straight line. Its velocities at A and B are respectively 7m/s^2 and 17m/s^2. M is the mid point of A and B. If t1is the time tajen to go from A to M and t2 is the time taken to go from M to B. Then what would be the ratio of t1/t2?

A particle is moving with a uniform acceleration along a straight line. Its velocities at A and B are respectively 7m/s^2 and 17m/s^2. M is the mid point of A and B. If t1is the time tajen to go from A to M and t2 is the time taken to go from M to B. Then what would be the ratio of t1/t2?

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
let total distance be x meter b/w A and B.
them to mid  – point the eqns. are:
(x/2) = 7*t1 + 0.5at1^2..............(1)
and
v = 7 + a*t1
 
For M to B
(x/2) = (a*t1 + 7)*t2 + 0.5*a*t2^2...............(2)
 
and
17 = 7 + a(t1 + t2) we get,
a(t1 + t2) = 10...........................(3)
sloving the three eqns. we get,
12(t1^2 – t2^2) = t1*t2
divide the whole eqn by t2^2 we get,
1.2(t1/t2)^2 – (t1/t2) – 1.2 = 0
let t1/t2 = x
then we get the quadratic,
1.2x^2 – x – 1.2 = 0
on solving x we get 
x = 1.5 or 3/2
that is the ratio,
t1/t2 = 3/2.

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