An insect moving along a straight line, travels in every second distance equal to the magnitude of time elapsed. Assuming acceeleration to be constant, and the insect starts at `t = 0`. Find the magnitude of initial velocity of insect.

Options

A. `(3)/(2)` unit
B. `(5)/(4)` unit
C. 2 unit
D. `(1)/(2)` unit

Answer

D

Explanation

Distance travelled from time 't - 1' sec to 't' sec is
`S = u + (a)/(2) (2 t - 1)` …(i)
from gives condition `S = t`…(ii)
from (i) and (ii), `t = u + (a)/(2) (2t - 1)`
`rArr u = (a)/(2) +t (1 - a)`
Since `u` and `a` are arbitary constants, and they must be constant for every time.
So, coefficient of `t` must be equal to zero.
`rArr 1-a = 0 rArr a = 1` for `a = 1, u = (1)/(2)` unit
Initial speed `= (1)/(2)` unit.