A particle starts from point A and travels along the solid curve shown in the figure. Determine approximately the position B of the particle such that the average velocity between positions A and B shares the same direction as the instantaneous velocity at B .

Step-by-step solution

The direction of average velocity between points A and B is along the secant line connecting A and B . The direction of instantaneous velocity at point B is along the tangent to the curve at B . For these two velocities to have the same direction, the secant line passing through A and B must be tangent to the curve at point B . From the given graph, the coordinates of the starting point A are approximately (1 m , 4 m ) . We can evaluate the given options by checking if the point lies on the curve and if the secant