Question

Two objects A and B accelerate from rest with the sameconstant acceleration. Object A accelerates for twice as muchas object B, however. Which one of the following statementsis true concerning these objects at the end of their respectiveperiods of acceleration?Object A will travel twice as far as object B.Object A will travel four times as far as object B.Object A will travel eight times further than object B.Object A will be moving four times faster than object B.Object A will be moving eight times faster than objectB.

Answer 1

Answer:

object A will travel  four times as far as object B.

Explanation:

The equation that describes the distance as a function of aceleration, initial speed and time is:

$x=v_{0}t+\frac{1}{2} at^2$

So,

$v_{0]=0$in both objects, because says accelerate from rest.

$t$ is the same for both objects.

The only diference is the time of acceleration, lets say $t_A$ be the time for object A, and $t_B$ be the time for object B.

Equation for object A

$x=\frac{1}{2} a{t_A]^2$

Equation for object B

$x=\frac{1}{2} a{t_B}^2$

If  $t_A=2*t_B$, then equation for object A is

$x=\frac{1}{2} a{t_A}^2=\frac{1}{2} a{(2*t_B)}^2=\frac{1}{2} a4{t_B}^2= 2 a{t_B}^2$

So comparing both equations, object A will travel  four times as far as object B.