Applications Of Derivatives Question 98
Question: If the path of a moving point is the curve $ x=at $ , $ y=b\sin at $ , then its acceleration at any instant
[SCRA 1996]
Options:
A) Is constant
B) Varies as the distance from the axis of x
C) Varies as the distance from the axis of y
D) Varies as the distance of the point from the origin
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Answer:
Correct Answer: C
Solution:
$ \frac{dx}{dt}=v_{x}=a\Rightarrow \frac{d^{2}x}{dt^{2}}=0=a_{x} $
$ a_{x} $ is acceleration in x-axis $ \frac{d^{2}y}{dt^{2}}=-ba^{2}\sin at\Rightarrow a_{y}=-a^{2}y $
Hence, $ a_{y} $ changes as y changes.
BETA
