A particle starts moving with acceleration 2 m/s². Distance travelled . . .

Question : A particle starts moving with acceleration 2 m/s². Distance travelled by it in 5th half second is 
(A) 1.25 m 
(B) 2.25 m 
(C) 6.25 m 
(D) 30.25 m 

Doubt by Tanishq

Solution : 

Here the language of the question is little bit tricky this why students and sometimes even teachers are not able to understand the question properly. 

Here we have to understand that 
First Half Second means - 0 sec to 0.5 sec

Second Half Second means - 0.5 sec to 1.0 sec
Third Half Second means - 1.0 sec to 1.5 sec
Fourth Half Second means - 1.5 sec to 2.0 sec 
& Fifth Half Second means - 2.0 sec to 2.5 sec

So we have first calculate distance from 0 to 2.5 sec and then from 0 to 2 sec and then subtract them. 

Here we can't use the Fourth Equation of Motion 
S_nth = u+a/2[2n-1]
Because it will work for full nth second and not for fractional value of second. 

So using 

s=ut+½at²
s₁=0(t)+½(2)(2)²
s₁=½(2)(2)²
s₁=4 m 

s=ut+½at²
s₂=0(t)+½(2)(2.5)²
s₂=½(2)(2.5)²
s₂=6.25 m 

Distance travelled by it in 5th half second is
S₂-S₁
=6.25-4
=2.25 m

Hence, (B) 2.25 m, would be the correct option.