Kinematics Question 166
Question: An insect moving along a straight line, travels in every second distance equal to the magnitude of time elapsed. Assuming acceleration to be constant, and the insect starts at $ t=0 $ . Find the magnitude of initial velocity of insect
Options:
A) $ \frac{3}{2}unit $
B) $ \frac{5}{4}unit $
C) $ 2unit $
D) $ \frac{1}{2}unit $
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Answer:
Correct Answer: D
Solution:
[d] distance travelled form time t-1 sec to t sec is $ S=u+\frac{a}{2}(2t-1) $
From given condition S=t (i) and (ii)
$ \Rightarrow t=u+\frac{a}{2}(2t-1) $
$ \Rightarrow u=\frac{a}{2}+t(1-a) $
Since u and a are arbitrary constants, and they must be constant for every time.
$ \Rightarrow $ coefficient of t must be equal to zero.
$ \Rightarrow $ $ 1-a=0\Rightarrow a=1 $ for $ a=1 $ , $ u=\frac{1}{2} $ unit Initial speed is $ \frac{1}{2} $ unit.
