Question

A point mass starts moving in a straight line with constant acceleration "$a$". At a time $t$ after the beginning of motion, the acceleration changes sign, without change in magnitude. Determine the time $t_0$ from the beginning of the motion in which the point mass returns to the initial position.

• A. $(2+\sqrt{3})t$
• B. $(2+\sqrt{2})t$
• C. $(3+\sqrt{2})t$
• D. $(12+\sqrt{2})t$

Answer 1

The correct option is B $(2+\sqrt{2})t$

let $s$ be the distance travled in time t

$s=\frac{a{t}^2}{2}\dots \left(1\right)$

let $t_1$ be the time in which it comes to its initial position

using equation of motion$s=ut+\frac{a{t}^2}{2}$

now $u=at,t=t_1,s=-s,a=-a$

$-s=\left(at\right)t_1-\frac{a{t}_1^2}{2}$

$s=-at{t}_1+\frac{a{t}_1^2}{2}\dots \left(2\right)$

using $\left(1\right)\&\left(2\right)$

$t_1^2-2t{t}_1-t^2$

solving $t_1=(\sqrt{2}+1)t$

$t_0=t_1+t$

$t_0=(\sqrt{2}+2)t$