21. A particle moves with uniform acceleration along
straight line AB.Its velocities at A and B are 2m/s
and 14 m/s respectively. M is the mid point of AB.If
the particle takes 2 seconds to go from A to M,
then time taken to travel from M to B is
(1) 1s
(2) 28
(3) 38
(4) 4s
Answers
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Answer:
1 s
Step-by-step explanation:
Total distance = S
From A to B
a = (v² - u²)/(2S)
= (14² - 2²)/(2S)
= 192/(2S)
= 96/S
From A to M
s = ut + 0.5at²
S/2 = (2 × 2) + (0.5a (2)²)
S/2 = 4 + 2a
S = 8 + 4a
S = 8 + (4 × 96/S)
S = (8S + 384)/S
S² = 8S + 384
S² - 8S - 384 = 0
On solving above quadratic equation we get
S = 24 or S = -16
Distance can't be negative. So take S = 24
So, acceleration is
a = 96/S
= 96/24
= 4 m/s²
From A to B
v = u + at
T = (v - u)/a
= (14 - 2) / 4
= 3 s
Time taken to travel from M to B
= Time taken from A to B - Time taken from A to M
= 3 s - 2 s = 1 s
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