In one-dimensional motion with constant acceleration and starting from rest, an object travels a distance $d$ in a time $t$. Which expression gives the acceleration $a$ in terms of $d$ and $t$?

• A. $a=\frac{d}{t^2}$
• B. $a=\frac{2d}{t}$
• C. $a=\frac{t^2}{2d}$
• D. $a=\frac{2d}{t^2}$

Answer: (D)

Verified step by step guidance

1. Identify the known variables and conditions: the object starts from rest, moves in one dimension with constant acceleration, covers a distance \(d\) in time \(t\), and we need to find the acceleration \(a\).
2. Recall the kinematic equation for displacement under constant acceleration starting from rest: \(d = \frac{1}{2} a t^{2}\).
3. Rearrange the equation to solve for acceleration \(a\): multiply both sides by 2 to get \$2d = a t^{2}$.
4. Isolate \(a\) by dividing both sides by \(t^{2}\), resulting in \(a = \frac{2d}{t^{2}}\).
5. This expression shows acceleration in terms of distance and time when starting from rest with constant acceleration.