Question

the position x of particle moving along x-axis varies with time t as x is equal to a Sin Omega T where a and omega are positive cons constant acceleration of a particle varies with the position access

Answer 1

After double differentiation
$d ^{2} x \div dt {}^{2} = a w {}^{2} - \sin(wt) \\ \: \: \: \: \: \: \: \: \: = - w {}^{2} \times a \sin(wt) \\ \: \: \: \: \: \: \: \: \: \: = - w {}^{2} x$

Answer 2

Acceleration occurs when the speed of an object changes, and the direction of the object changes.

Mathematically the expression for acceleration is given by

Acceleration: $(a)=(V_f -V_i)/t$

where,

$v_f$ is the final velocity and

$v_i$ is the initial velocity.

The unit for acceleration is SI unit is m/s/s or $m/s^2$.

Here,

                       $d^2x/dt^2= a\omega^2-sin(\omega t)\\=-\omega^2\times asin\omega t =-\omega^2x$