Given
\(V = 2t\hat i + 3t\hat j\)
\(V_x = 2t\)
\(\frac{dx}{dt} = 2t\)
\(\int dx = \int 2t\,dt\)
\(x = \frac{2t^2}2 + c\)
\(x = t^2 +c\)
at t = 0 x = 0 hence c = 0
\(x = t^2\)
\(V_y = 3t\)
\(\frac{dy}{dt} = 3t\)
\(\int dy = \int 3t\,dt\)
\(y = \frac{3t^2}2 + c\)
y = 0 t = 0 hence c = 0
\(y = \frac{3t^2}2\)
\(y = \frac{3\times x}2\)
\(2y -3 x = 0\)
