Solve the equation for \( a \).
\[ D = vt + \frac{1}{2}at^2 \]
Answer (3)
D = v t + 2 1 a t 2 2 1 a t 2 + v t = D / − v t 2 1 a t 2 = D − v t / ⋅ 2 a t 2 = 2 D − 2 v t / : t 2 a = t 2 2 D − 2 v t
D = vt + 1/2at^2 D - vt = 1/2at^2 2(D - vt)/t^2 = a
To solve for a in the equation D = v t + 2 1 a t 2 , we first rearrange it to isolate a on one side. The final formula for a is a = t 2 2 ( D − v t ) . This shows how acceleration is related to distance, initial velocity, and time.
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