Question

Two objects A and B accelerate from rest with the same constant acceleration. Object A accelerates for twice as long 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 four times a5 far a5 object B (b) Object A will travel twice a5 far a5 object B (c) Object A will travel nine times as faras object B (d) Object A wiil bejmnoving tWO times faster than obiect R

Answer 1

The correct answer is (b) Object A will travel twice as far as object B.

Here's why:

Let's call the acceleration of both objects "a" and the time for which object B accelerates "t". Since object A accelerates for twice as long as object B, the time for which object A accelerates is "2t".

Using the equations of motion, we can find the distance traveled by each object during their respective periods of acceleration.

For object B:
distance = (1/2)at^2

For object A:
distance = (1/2)a(2t)^2 = 2at^2

Substituting the values of distance for each object, we get:

distance traveled by object B = (1/2)at^2
distance traveled by object A = 2at^2

Dividing the distance traveled by object A by the distance traveled by object B gives:

(2at^2) / [(1/2)at^2] = 4

Therefore, object A will travel four times as far as object B. Hence, the correct answer is (a).