Differential Equations Question 321
Question: A particle starts at the origin and moves along the x-axis in such a way that its velocity at the point (x, 0) is given by the formula $ \frac{dx}{dt}={{\cos }^{2}}\pi x. $ Then the particle never reaches the point on
[AMU 2000]
Options:
A) $ x=\frac{1}{4} $
B) $ x=\frac{3}{4} $
C) $ x=\frac{1}{2} $
D) x = 1
Show Answer
Answer:
Correct Answer: C
Solution:
Given $ \frac{dx}{dt}={{\cos }^{2}}\pi x $ . Differentiate w.r.t. t, $ \frac{d^{2}x}{dt^{2}}=-2\pi \cos \pi x \sin \pi x $
$ \because $ $ \frac{d^{2}x}{dt^{2}}=0 $
Therefore $ -2\pi \sin 2\pi x=0 $
Therefore $ \sin 2\pi x=\sin \pi x $
Therefore $ 2\pi x = \pi $
Therefore $ x=1/2 $ .
BETA
