Starting from rest a lady bug runs along a straight line with constant acceleration. After time T1 , the lady bug suddenly reverses the direction of its acceleration but keeps the magnitude of the acceleration constant and the same as it was before.
How much time (in terms of T1) would it take the ladybug to get back to its starting point from the place where it turned around?
Best Answer
The following is a Physics-oriented, more or less formula-free solution. When the acceleration changes, the velocity still goes the wrong way. By symmetry, after a further time $T_1$, the ladybug is at rest, twice as far from its starting point as the distance from the starting point to the place it stepped on the brakes.
So now it has twice that distance to traverse. Distance travelled from rest, under constant acceleration, is proportional to the square of time. So the time required to get back to the starting point from the furthest point reached is $\sqrt{2}\,T_1$. Total time from the time the acceleration reversed is therefore $T_1+\sqrt{2}\,T_1$.