When an object is stationary and begins to move at a constant acceleration, the square of the velocity is twice the product of the acceleration and the distance traveled. If an object travels at a constant acceleration of 10 m/s² for 45 m, what is its velocity, in meters per second?
Explanation
First, translate the statement: the square of the velocity is twice the product of the acceleration and the distance traveled. Let the velocity be represented by v, the acceleration be represented by a, and the distance be represented by d. Translate this one piece at a time. First, the square of the velocity translates to \(v^{2}\). The word is translated to =. The word twice translates to 2 times whatever follows. What follows is the product of the acceleration and the distance traveled. Since product translates to multiplication, this translates to \(a \times d\). Twice this is 2ad. Therefore, the statement translates to \(\mathrm{v}^{2}=2 \mathrm{ad}\). The question states that a = 10 and d = 45, so plug in these values to get \(v^{2}=2(10)(45), \text { so } v^{2}=900\). Take the square root of both sides to get v = 30. The correct answer is (A).
