Answer to Question #192039 in Mechanics | Relativity for Nicole

Question

Two objects, X and Y, accelerate from rest with the same constant acceleration. Object X accelerates for three times the amount of time as object Y. Which of the following is true of these objects at the end of their respective periods of acceleration?

(A) The final speed of object X is the same as object Y. 

(B) The final speed of object X is three times faster than object Y.

(C) Object X has traveled twice as far as object Y.

(D) Object X has traveled four times as far as object Y.

Answer 1

Let speed of object X be $v_x$

Let speed of object Y be $v_y$

Let acceleration be $a$

Let time of acceleration of object X be $t_x$

Let time of acceleration of object Y be $t_y$

$v_y=0+at_y$

$t_y=\dfrac{v_y}{a}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(1)$

$v_x=0+at_x$

$t_x=\dfrac{v_x}{a}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(2)$

$t_x=3t_y\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(3)$

from equation (1),(2) and (3)

$v_x=3v_y$

$\therefore$ The final speed of object X is three times faster than object Y

$v_x^2=2as_x$

$v_y^2=2as_y$

$v_x^2=9v_y^2$

$\therefore \space s_x=9s_y$

Object X has travelled nine times as far as object Y