Which of the following equations can be used to solve for $a$?

• A. $v=u+at$
• B. $F=ma$
• C. $s=ut+\frac{1}{2}a{t}^2$
• D. $a=\frac{v-u}{t}$

Answer: (D)

Verified step by step guidance

1. Identify the variable you want to solve for, which is acceleration \( a \).
2. Look at each given equation and determine if it can be rearranged to isolate \( a \).
3. From the first equation \( v = u + a t \), rearrange to solve for \( a \): subtract \( u \) from both sides to get \( v - u = a t \), then divide both sides by \( t \) to isolate \( a \), resulting in \( a = \frac{v - u}{t} \).
4. Check the second equation \( F = m a \). You can also solve for \( a \) by dividing both sides by \( m \), giving \( a = \frac{F}{m} \), but this depends on knowing the force and mass, not velocity or time.
5. The third equation \( s = u t + \frac{1}{2} a t^2 \) can be rearranged to solve for \( a \) by isolating the term with \( a \), subtracting \( u t \) from both sides, then multiplying both sides by \( \frac{2}{t^2} \), resulting in \( a = \frac{2(s - u t)}{t^2} \).