Question

As the particle passes through the point (4,2), its x-coordinate increases at a rate of 7 cm/s. How fast is the distance from the particle to the origin changing at this instant?

Answer 1

hint:
we have the subsequent position function:
\[x\left( t \right) = 7t + C\]

Answer 2

where C is a constant to be determined using the initial conditions

Answer 3

we know that at t=0, x=4, so we can write:
\[\begin{gathered}
4 = x\left( 0 \right) = 7 \cdot 0 + C = C \hfill \\
C = 4 \hfill \\
\end{gathered} \]

Answer 4

so our position fuction will be this:
\[x\left( t \right) = 7t + 4\]