Question

FigureA particle starts from a point A and travels along the solid curve shown in figure (3−E7). Find approximately the position B of the particle such that the average velocity between the position A and B has the same direction as the instantaneous velocity at B.

Answer 1

Answer:

At position B instantaneous velocity has direction along BC . For average velocity between A and B. Vave = displacement / time = ( vector AB/ t) t = time We can see that vector AB is along vector BC i.e. they are in same direction. The point is B (5m, 3m)

Answer 2

The position B of the particle is (5 m, 3 m).

Explanation:

The instantaneous velocity at position B has direction along BC.

For average A to B velocity :

               $\mathrm{V}_{\mathrm{avg}}=\frac{\text {displacement}}{\text {time}}=\frac{\text { vector } \mathrm{AB}}{t}$

                     t = time  

We can see that vector AB is in the same direction along vector BC i.e.. The point is with B (5 m, 3 m).

Instantaneous velocity :

• Instant velocity is the velocity of an object moving at a given point in time.

• This is equivalent to average velocity, but we limit the time period so that it approaches zero.        

Therefore, the point B is (5 m , 3 m).