Question

The acceleration of a particle is given by the $\mathrm{a}=\mathrm{X}$ where $\mathrm{X}$ is a constant. if the particle starts at origin from rest. its distance from origin after time t is given by.

Answer 1

Hint: From the equation, ${S}={ut}+\dfrac{1}{2}{a}{{{t}}^{2}}$, we can determine the solution of the given question, but from the given question, \[~ut\to 0\] as initial velocity(u) is 0. Therefore, distance $=\dfrac{1}{2}{a}{{{t}}^{2}}$. Keeping this in mind, we can proceed further to finding out the solution.

Complete step by step answer:
From the given question,
We can obtain the given acceleration $\mathrm{a}=\mathrm{X}(\mathrm{X}=\mathrm{constant})$
Therefore, the body travels in a linear motion.
Hence, it can be determined that the modulus of displacement is equivalent to the distance, which can also be represented as,
$\mid {displacement}\mid {=distance}$
From these equations, we can calculate the distance after time t as,
distance $=\mathrm{ut}+\dfrac{1}{2} \mathrm{at}^{2}$ as the particle initially starts accelerating from rest $\Rightarrow \mathrm{u}=0$

Therefore, the distance from origin after time t is $=\dfrac{1}{2} \mathrm{Xt}^{2}$.

Note: Equation of motion, a numerical recipe that depicts the position, velocity, or acceleration of a body comparative with a given edge of reference. Newton's second law, which expresses that the force F following up on a body is equivalent to the mass m of the body increased by the acceleration a of its focal point of mass, F = ma, is the fundamental equation of motion in traditional mechanics. In the event that the force following up on a body is known as a component of time, the speed and position of the body as elements of time can, hypothetically, be gotten from Newton's equation by a cycle known as integration.