Question

A particle moves in XY plane such that its position, velocity and acceleration are given by $\overrightarrow{r}=x\hat{i}+y\hat{j};\overrightarrow{v}=v_x\hat{i}+v_y\hat{j};\overrightarrow{a}=a_x\hat{i}+a_y\hat{j}$
which of the following condition is correct if the particles speed is reducing?

• A. $x{v}_x+y{v}_x<0$
• B. $x{v}_x+y{v}_y+y{v}_y>0$
• C. $a_x{v}_x+a_y{v}_y<0$
• D. $a_x{v}_x+a_y{v}_y>0$

Answer 1

The correct option is C $a_x{v}_x+a_y{v}_y<0$

For speeding down, the velocity and acceleration vector should have opposite sign
$\overrightarrow{a}.\overrightarrow{v}<0\Rightarrow a_x{v}_x+a_y{v}_y<0$