Question

An object initially at rest accelerates for 22 s. Its final position is 30 m from its initial position at the end of the acceleration. What acceleration did it experience?

A) 1.36 m/s²
B) 1.48 m/s²
C) 1.64 m/s²
D) 1.72 m/s²

Answer 1

1.64 m/s²acceleration was experienced. Thus the correct option is C. 1.64 m/s².

Step-by-step explanation:

The acceleration experienced by the object can be determined using the kinematic equation:
`\[ \Delta x = v_0 t + (1)/(2) a t^2 \]`, where
`\( \Delta x \)` is the displacement,
`\( v_0 \)` is the initial velocity (which is 0 since the object is initially at rest),
`\( t \)` is the time of acceleration, and
`\( a \)` is the acceleration. Rearranging the equation to solve for acceleration, we get
`\[ a = (2(\Delta x))/(t^2) \]`. Substituting the given values,
`\[ a = (2(30\, m))/((22\, s)^2) \].` Calculating this expression results in an acceleration of approximately
`\(1.64\, m/s^2\).`

This acceleration represents the rate at which the object's velocity is changing. In simpler terms, it describes how fast the object is gaining speed in each second. The positive value indicates that the acceleration is in the same direction as the motion, confirming that the object is moving away from its initial position.

Therefore, the correct answer to the question is option C)
`\(1.64\, m/s^2\)`, reflecting the magnitude of the acceleration. This process of using kinematic equations to find acceleration is fundamental in physics and helps to understand the motion of objects under the influence of external forces.

Thus the correct option is C. 1.64 m/s².