1956 AMC 12 Problem 40

Attempt Problem 40 of the 1956 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1956 AMC 12 solutions, or check the answer key.

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40.

If

V=gt+V_0

and

S=\dfrac12gt^2+V_0t,

then

t

equals:

\dfrac{2S}{V+V_0}

\dfrac{2S}{V-V_0}

\dfrac{2S}{V_0-V}

\dfrac{2S}{V}

2S-V

Answer: A

Concepts:kinematics formulas algebraic elimination average velocity

Difficulty rating: 1530

Small hint:

Use the first equation to replace

gt

in the second

Big hint:

Factor

t

after writing

gt=V-V_0

Solution:

From the first equation,

gt=V-V_0.

Therefore

\begin{aligned} S&=\frac12(gt)t+V_0t\\ &=\frac12(V-V_0)t+V_0t\\ &=\frac12(V+V_0)t. \end{aligned}

Solving gives

t=\frac{2S}{V+V_0}.

Thus, the correct answer is A.

Problem 40 in other years