Question

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
​

Answer 1

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