A particle moves in the xy-plane so that its position for t ≥ 0 is given by the parametric equations x = ln (t + 1) and y = k(t^2) , where k is a positive constant. The line tangent to the particle’s path at the point where t = 3 has slope 8. What is the value of k ?

Answer 1

dy/dx = dy/dt / dx/dt = 2kt(t+1)
So, at t=3, dy/dx = 24k = 8
so, k = 1/3