Question

The velocity of a particle on the x-axis is given by the differential equation. dx/dt = 3/4t^(1/2). The particle is at x = 5, when t = 1. The position of the particle as a function of time is x(t) = ___.

Answer 1

Do you mean \( \frac{dx} {dt}\)

Answer 2

Oh sorry, yea i do

Answer 3

\[
x(t)=\int \frac{3 \sqrt{t}}{4} \, dt=\frac{t^{3/2}}{2}+C\\
5=x(1)= \frac 1 2 +C\\
C=\frac 92\\
x(t)=\int \frac{3 \sqrt{t}}{4} \, dt=\frac{t^{3/2}}{2}+\frac 9 2\\
\]