In Physics, acceleration of an object can be found using the formula \( a=\frac{v-u}{t} \), where \( a \) is the acceleration, \( v \) is the final velocity, \( u \) is the initial velocity, and \( t \) is time. Which equation correctly solves for the initial velocity? A \( u=a t-v \) B \( u=\frac{a}{t}-v \) C \( u=\frac{t}{a}-v \) D \( u=v-a t \)

To solve for the initial velocity \( u \), you can rearrange the formula \( a=\frac{v-u}{t} \). By multiplying both sides by \( t \) and then rearranging, you arrive at \( u = v - a t \). So, the correct answer is **D \( u = v - a t \)**. Acceleration has not only a physical meaning but also a historical one. Sir Isaac Newton formulated the laws of motion in the 17th century, fundamentally changing the way we understand movement. His groundbreaking work, including the second law \( F=ma \), laid the groundwork for classical mechanics, making it pivotal for both theoretical and practical physics. In the real world, knowing initial velocity is crucial in various fields, from automotive safety to space exploration. Engineers calculate initial speeds to design safer vehicles, ensuring they can withstand crashes effectively. Similarly, spacecraft trajectories are meticulously calculated using initial velocity to ensure successful launches and orbit insertions, making this formula vital for modern technology.