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.

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gennerandrescarrillo gennerandrescarrillo · Answer 1 · 2019-09-26T02:45:47+02:00

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:

[tex]x=v_{0}t+\frac{1}{2} at^2[/tex]

So,

[tex]v_{0]=0[/tex]in both objects, because says accelerate from rest.

[tex]t[/tex] is the same for both objects.

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

Equation for object A

[tex]x=\frac{1}{2} a{t_A]^2[/tex]

Equation for object B

[tex]x=\frac{1}{2} a{t_B}^2[/tex]

If [tex]t_A=2*t_B[/tex], then equation for object A is

[tex]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[/tex]

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