A body starts from rest and moves with constant acceleration for t seconds

CBSE Class 11
1

A body starts from rest and moves with constant acceleration for t seconds. It travels a distance X1 in first half of time and X2 in second half of time. Then which one is correct?

  1. X2=X1
  2. X2=2X1
  3. X2=3X1
  4. X2=4X1
2

The distance traveled with constant acceleration in a given time t is, " S = u×t + (1/2)×a×t2",
For the first half time, initial speed u=0, hence distance X1 = (1/2)×a×(t/2)2 = (1/8)×a×t2 …(1)
for second half time, initial speed = a×(t/2), hence distance X2 = a×(t/2)×(t/2) + (1/2)×a×(t/2)2 = (3/8)×a×t2 …(2)
from (1) and (2), we can write X2 = 3 × X1