In the case considered in the question (14), show what the trajectory corresponds to in case the magnitude of acceleration is \(a=2 k \sqrt{1+\frac{t}{T}}\), where \(T=\) cost.

Question 14

A particle moves on a predetermined trajectory with the equation of motion \(s(t)=k t^{2}\), with \(k\) constant and with magnitude of the acceleration equal to \(a=2 k\). Show by using (3.74) that the radius of curvature is given by the relation \(ho=\frac{v^{2}}{\sqrt{a^{2}-\stackrel{s}{s}^{2}}}\). Show that in the present case the motion is rectilinear.

u2 a = v + p P (3.74)