Two objects A and B accelerate from rest with the same constant acceleration. Object A accelerates for twice as much time as object B, however. Which one of the following statements is true concerning these objects at the end of their respective periods of acceleration?
A)Object A will travel twice as far as object B.
B)Object A will travel four times as far as object B.
C)Object A will travel eight times further than object B.
D)Object A will be moving four times faster than object B.
E)Object A will be moving eight times faster than object B.

Question

Quizplus · Accepted Answer

Let's assume that both objects have an initial velocity of 0 and a constant acceleration of a. Let's also assume that object B accelerates for a time t, meaning that object A accelerates for a time 2t (twice as much time as object B).

Using the kinematic equation for displacement, we can find the distance traveled by each object during their respective periods of acceleration:

Distance traveled by object A: 
dA = 1/2 * a * (2t)^2 
dA = 2 * (1/2 * a * t^2)
dA = 2 * dB

Distance traveled by object B: 
dB = 1/2 * a * t^2

Therefore, at the end of their periods of acceleration, object A will have traveled four times as far as object B (dA = 2 * dB). Thus, the correct answer is B.

Two Objects a and B Accelerate from Rest with the Same