question_answer

An object travels along a path shown with changing velocity as indicated by vectors A and B. Which vector best represents the net acceleration of the object from time \[{{t}_{A}}\] to \[{{t}_{B}}\]?

A)    

B)

C)  

D)

Correct Answer: D

Solution :

The direction of acceleration is the same as the direction of the changes in velocity, according to \[A=\frac{{{v}_{f}}-{{v}_{i}}}{t}.\] Because \[\Delta v={{v}_{f}}-{{v}_{i}},\] we can determine \[\Delta v\]graphically by adding \[{{v}_{f}}\] to the negative of \[{{v}_{i}},\] or \[B+(-A).\] Placing the B vector ?tip-to-tail? with the \[-A\]vector gives a direction for \[\Delta \,v\](and therefore, a) to the left