Question

If the path of a moving point is the curve $x = aty = b\sin at$, then its acceleration at any instant

• 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 of the point from the origin

Answer 1

Answer: (C)

Varies as the distance from the axis of y

Answer 2

$\frac{dx}{dt} = v_{x} = a$ ⇒ $\frac{d^{2}x}{dt^{2}} = 0 = a_{x}$

$a_{x}$ is acceleration in x-axis

$\frac{d^{2}y}{dt^{2}} = - ba^{2}\sin at$ ⇒ $a_{y} = - a^{2}y$

Hence, $a_{y}$ changes as y changes.