A transverse wave along a string is given by y-2sin2-3t-x-4- where x and y are in cm and t is in second- The acceleration of a particle located at X - 4 cm at t - 1 sec is -

The $x$ and $y$ coordinates of the particle at any time are $x = 5 t - 2 t^{2}$ and $y = 10 t$ respectively, where $x$ and $y$ are in meters and $t$ in seconds. The acceleration of the particle at $t = 2 s$ is

Q. A particle moves along a curve whose parametric equations are:

x = t^{3} + 2 t, y = - 3 e^{- 2 t} a n d z = 2 s i n (5 t)

, where x, y and z show variations of the distance covered by the particle (in cm) with time t (in s). The magnitude of the acceleration of the particle

(i n c m / s^{2} a t t = 0)

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A transverse wave along a string is given by y=2sin(2π(3t−x)+π4), where x and y are in cm and t is in second. The acceleration of a particle located at X=4 cm at t=1 sec is :

The correct option is D −36√2π2cm/s2y=2 sin(6πt−2πx+π4)vp=dydt=12π cos(6πt−2πx+π4)ap=dvpdt =−72π2 sin(6πt−2πx+π4)At x=4, t=1ap=−72π2 sin(6π−8π+π4) =−72π2×1√2 =−36√2π2 cm/sec2

A transverse wave along a string is given by $y = 2 sin (2 π (3 t - x) + \frac{π}{4})$ , where $x$ and $y$ are in $c m$ and $t$ is in $s e c o n d$ . The acceleration of a particle located at $X = 4 c m$ at $t = 1 s e c$ is :