Question

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) 2s
(3) 3
(4) 45
​

Answer 1

Answer:

Explanation:

=> Here, 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.

v²=u²+2as  

v² = 2² + 2as

v² - 4 = 2as ...(1)

14² = v² + 2as

196 - v² = 2as ...(2)

From eq (1) and (2), we get

196 - v² = v² - 4

2v² = 200

v² = 100

v = 10 m/s.

=> time taken to travel from A to M

v = u + at1

t1 = v - 2 / a

= 10 - 2 / a

= 8 / a

=> time taken to travel from M to B

t2 = 14 - v / a

14 - 10 / a

= 4 / a

=> t2 / t1 = 4/a / 8/a = 1 / 2 a

Thus,  time taken to travel from M to B is 1s.