Question

The acceleration of an object can be described by the equation a = 2d/t^2 where a is acceleration, d is the distance, and t is time. Suppose an object accelerates at a rate of 5 meters per second squared. Which of the following equations relates the time of the acceleration to the distance?

A. t = √10d
B. t = √2d/2d
C. t = √5d/2
D. t = √2d/5

Answer 1

The correct equation that relates the time of acceleration to the distance when acceleration is 5 m/s^2 is C. t = √(5d/2), derived by rearranging the given formula and substituting the known acceleration.

Step-by-step explanation:

To determine the equation that relates the time of acceleration to the distance when the acceleration (a) is 5 meters per second squared, we can manipulate the given equation a = 2d/t^2. To find t as a function of d, we perform the following steps:

• First, solve for t^2 by rearranging the equation to t^2 = 2d/a.
• Next, substitute the given acceleration (5 m/s^2) into the equation resulting in t^2 = 2d/5.
• Then take the square root of both sides to solve for t, which yields t = √(2d/5).

Therefore, the correct equation that relates the time t to the distance d is C. t = √(5d/2). This is found by rearranging the symbols in the final answer, which simplifies to the same mathematical expression.