Assume that the body slides down the plane from rest, i.e. u = 0. Let 'h' be the total distance (length) of the inclined plane.
Case I: The body covers
distance in time t = 2 s
Using the second equation of motion: S = ut +
at2, where
S =
; distance covered
t = 2 s: time taken
u = 0: initial velocity
a: acceleration of the block
⇒
= 0 +
a×22 ⇒ h = 8a ... (i)
Case Ii: The body covers the distance of the complete inclined planeDistance covered, S = h; f = time taken and initial velocity, u = 0.
Using the same equation of motion, we obtain
h = 0 +
at2 ... (ii)
Equating eqs. (i) and (ii), we get
8a =
at2 ⇒ t' =
√16s = 4s
Therefore, time taken by the body to cover the total distance of the inclined plane is 4 s.
Hence, option 'A' is correct.