Question

A particle starts from the origin at t=8 and moves in the x-y plane with constant acceleration a in the direction. Its equation of notion is $y=b{x}^2$. The x component of its velocity is:

• A. (a) Variable
• B. (b) $\sqrt{\frac{2a}{b}}$
• C. (c)$\frac{a}{2b}$
• D. (d)$\sqrt{\frac{a}{2b}}$

Answer 1

The correct option is A (a) Variable

The right option is A.

We have,

$t=8s$

The equation of motion is $y=b{x}^2$

So, Let the angle made by the slope be A,

$tanA=\frac{dy}{dx}=2bx$

$A=ta{n}^{-1}\left(2bx\right)$

x component of motion $=cos\left(A\right)$

Which is variable because particle velocity is the velocity of a particle (real or imagined) in a medium as it transmits a wave. The SI unit of particle velocity is the meter per second (m/s).

In many cases, this is a longitudinal wave of pressure as with sound, but it can also be a transverse wave as with the vibration of a taut string.