If the displacement in the x-direction is dx = 4t, what would you plug in for t in dy = v0,y t + 1/2ay t2?dx / 2dx / 4 -dx / 44 / dx

To solve the given expression, we need to analyze and simplify it step by step. Here's how we approach this problem:

1. Break Down the Problem

We have the following:

• Displacement in the x-direction: $dx = 4t$
• The expression we need to work with: $dy = v_{0,y} t + \frac{1}{2} a_y t^2$

2. Relevant Concepts

• First, we need to express $t$ in terms of $dx$.
• We'll then plug $t$ into the equation for $dy$.
• The expression provided seems to involve several operations with $dx$; we'll clarify these as we move along.

3. Analyze and Detail

From the equation $dx = 4t$, we can express $t$ as: $t = \frac{dx}{4}$

Next, we'll substitute this value of $t$ into the expression for $dy$: $dy = v_{0,y} \left(\frac{dx}{4}\right) + \frac{1}{2} a_y \left(\frac{dx}{4}\right)^2$

4. Verify and Summarize

Now we'll rewrite the equation: $dy = v_{0,y} \cdot \frac{dx}{4} + \frac{1}{2} a_y \cdot \frac{dx^2}{16}$ This simplifies to: $dy = \frac{v_{0,y}}{4} dx + \frac{a_y}{32} dx^2$

Final Answer

Thus, when $t$ is given the value of $\frac{dx}{4}$, the expression for $dy$ becomes: $dy = \frac{v_{0,y}}{4} dx + \frac{a_y}{32} dx^2$